Edit Profile Chaplain, Mark A. J. Compute Distance To: Compute Author ID: chaplain.mark-a-j Published as: Chaplain, M. A. J.; Chaplain, Mark; Chaplain, Mark A. J. Homepage: http://www.mcs.st-andrews.ac.uk/~majc/ External Links: MGP · Wikidata · ORCID · ResearchGate · dblp · GND Documents Indexed: 157 Publications since 1990, including 5 Books all top 5 Co-Authors 4 single-authored 33 Xu, Rui 27 Davidson, Fordyce A. 19 Anderson, Alexander R. A. 13 Byrne, Helen Mary 9 Lorenzi, Tommaso 9 McDougall, Steven R. 8 Trucu, Dumitru 7 Gerisch, Alf 7 Hubbard, Stephen F. 7 Schofield, Pietà G. 5 Chen, Lansun 5 Matzavinos, Anastasios 5 Stéphanou, Angélique 4 Domschke, Pia 4 Orme, Michelle E. 4 Sleeman, Brian D. 4 Sturrock, Marc 3 Burgess, Andrew E. F. 3 Enderling, Heiko 3 Feltham, Daniel L. 3 Gourley, Stephen A. 3 Lolas, Georgios 3 Lowengrub, John Samuel 3 Macfarlane, Fiona R. 3 Macnamara, Cicely K. 3 Maini, Philip Kumar 3 Preziosi, Luigi 3 Sherratt, Jonathan A. 3 Szymańska, Zuzanna 3 Thompson, Alastair M. 3 Valenciano, José 2 Andasari, Vivi 2 Bellomo, Nicola 2 Bitsouni, Vasiliki 2 Britton, Nicholas Ferris 2 Britton, Nick F. 2 Cristini, Vittorio 2 Devlin, A. H. 2 Eftimie, Raluca 2 Gordon, Kirsty E. 2 Hill, Lydia A. 2 Kuznetsov, Vladimir A. 2 Lachowicz, Mirosław 2 Lin, Ping 2 Liu, Sijia 2 Lorz, Alexander 2 Mcelwain, D. L. Sean 2 Mitchell, C. A. 2 Mitchell, Elaine I. 2 Munro, Alastair J. 2 Panetta, John Carl 2 Pearce, Ian G. 2 Pettet, Graham J. 2 Powathil, Gibin G. 2 Stuart, Andrew M. 2 Terry, Alan J. 2 Tracqui, Philippe 2 Vaidya, Jayant S. 2 Venkataraman, Chandrasekhar 1 Adam, John A. 1 Aldakheel, Sahar 1 Aubert, M. 1 Banerjee, Sayanti 1 Benson, Debbie L. 1 Bingham, Richard 1 Cameron, David C. 1 Chauvet, Pierre 1 Crawford, John W. 1 Cytowski, Maciej 1 De Angelis, Elena 1 Dettmann, Carl P. 1 Dosi, Giovanni 1 El Akili, I. 1 Evans, Diane L. 1 Forni, Guido 1 Franssen, Linnea C. 1 Frieboes, Hermann B. 1 Ganesh, Madhu 1 Giles, Susan M. 1 Giverso, Chiara 1 Graham, Ivan G. 1 Graziano, L. 1 Griffiths, David F. 1 Hellander, Andreas 1 Hodgkinson, Arran 1 Hofer, Thomas 1 Hopkinson, I. 1 James, Z. H. 1 Jarvis, R. J. 1 Joshi, Badal 1 Kapelyukh, Yury 1 Keener, James P. 1 Knopoff, Damian A. 1 Laín, S. 1 Lejeune, Olivier 1 Lewis, Mark Alun 1 Macklin, Paul 1 Madzvamuse, Anotida 1 Marciniak-Czochra, Anna K. 1 McLachlan, John C. ...and 41 more Co-Authors all top 5 Serials 19 Journal of Theoretical Biology 13 Journal of Mathematical Biology 13 Bulletin of Mathematical Biology 12 Applied Mathematics and Computation 12 Mathematical and Computer Modelling 9 Applied Mathematics Letters 8 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 Mathematical Biosciences 6 IMA Journal of Mathematics Applied in Medicine and Biology 5 Journal of Theoretical Medicine 4 Journal of Mathematical Analysis and Applications 4 Mathematical Medicine and Biology 4 Mathematical Modelling of Natural Phenomena 2 Applicable Analysis 2 Multiscale Modeling & Simulation 2 Mathematical Biosciences and Engineering 1 Computers & Mathematics with Applications 1 IMA Journal of Applied Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Statistical Physics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Chaos, Solitons and Fractals 1 Kyungpook Mathematical Journal 1 Mathematische Nachrichten 1 Acta Mathematicae Applicatae Sinica. English Series 1 Numerical Methods for Partial Differential Equations 1 European Journal of Applied Mathematics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 Communications on Applied Nonlinear Analysis 1 Differential Equations and Dynamical Systems 1 Journal of Biological Systems 1 The ANZIAM Journal 1 Nonlinear Analysis. Real World Applications 1 Nonlinear Functional Analysis and Applications 1 Dynamical Systems 1 Discrete and Continuous Dynamical Systems. Series B 1 Forma 1 Journal of Applied Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Lecture Notes in Mathematics 1 IAS/Park City Mathematics Series 1 Networks and Heterogeneous Media 1 Modeling and Simulation in Science, Engineering and Technology all top 5 Fields 154 Biology and other natural sciences (92-XX) 73 Partial differential equations (35-XX) 35 Ordinary differential equations (34-XX) 23 Numerical analysis (65-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Mechanics of deformable solids (74-XX) 3 General and overarching topics; collections (00-XX) 3 Probability theory and stochastic processes (60-XX) 2 Difference and functional equations (39-XX) 2 Computer science (68-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Systems theory; control (93-XX) 1 Topological groups, Lie groups (22-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 134 Publications have been cited 2,716 times in 1,416 Documents Cited by ▼ Year ▼ Continuous and discrete mathematical models of tumor-induced angiogenesis. Zbl 0923.92011Anderson, A. R. A.; Chaplain, M. A. J. 202 1998 Growth of nonnecrotic tumors in the presence and absence of inhibitors. Zbl 0836.92011Byrne, H. M.; Chaplain, M. A. J. 146 1995 Growth of necrotic tumors in the presence and absence of inhibitors. Zbl 0856.92010Byrne, H. M.; Chaplain, M. A. J. 116 1996 Mathematical modelling of cancer cell invasion of tissue: the role of the urokinase plasminogen activation system. Zbl 1094.92039Chaplain, M. A. J.; Lolas, G. 115 2005 Mathematical modelling of tumour invasion and metastasis. Zbl 0947.92012Anderson, A. R. A.; Chaplain, M. A. J.; Newman, E. L.; Steele, R. J. C.; Thompson, A. M. 87 2000 Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Zbl 1108.92023Chaplain, M. A. J.; Lolas, G. 84 2006 Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. Zbl 1397.92326Gerisch, A.; Chaplain, M. A. J. 78 2008 Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development. Zbl 0859.92012Chaplain, M. A. J. 67 1996 Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. Zbl 0988.92003Chaplain, M. A. J.; Ganesh, M.; Graham, I. G. 66 2001 Multiscale modelling and nonlinear simulation of vascular tumour growth. Zbl 1311.92040Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 63 2009 A new mathematical model for avascular tumour growth. Zbl 0990.92021Sherratt, Jonathan A.; Chaplain, Mark A. J. 63 2001 A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. Zbl 0783.92019Chaplain, M. A. J.; Stuart, A. M. 61 1993 Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Zbl 0883.92014Byrne, H. M.; Chaplain, M. A. J. 59 1996 Free boundary value problems associated with the growth and development of multicellular spheroids. Zbl 0906.92016Byrne, H. M.; Chaplain, M. A. J. 58 1997 Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Zbl 1098.92037Chaplain, M. A. J.; Graziano, L.; Preziosi, L. 57 2006 Mathematical modelling of cancer invasion of tissue: the role and effect of nonlocal interactions. Zbl 1171.35066Szymańska, Zuzanna; Rodrigo, Cristian Morales; Lachowicz, Mirosław; Chaplain, Mark A. J. 56 2009 Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Zbl 1334.92106McDougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J.; Sherratt, J. A. 47 2002 Mathematical modelling of the spatio-temporal response of cytotoxic \(T\)-lymphocytes to a solid tumour. Zbl 1061.92038Matzavinos, Anastasios; Chaplain, Mark A. J.; Kuznetsov, Vladimir A. 46 2004 Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. Zbl 1230.92022Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P.; Chaplain, Mark A. J. 42 2011 Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions. Zbl 0812.92011Byrne, H. M.; Chaplain, M. A. J. 39 1995 Mathematical modelling of tissue invasion. Zbl 1337.92103Chaplain, Mark A. J.; Anderson, Alexander R. A. 35 2003 Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns. Zbl 1303.92043Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J. 33 2014 Mathematical modelling of cancer invasion: the importance of cell – cell adhesion and cell – matrix adhesion. Zbl 1221.35189Chaplain, Mark A. J.; Lachowicz, Mirosław; Szymańska, Zuzanna; Wrzosek, Dariusz 33 2011 Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments. Zbl 1066.92059Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 33 2004 A mathematical model for capillary network formation in the absence of endothelial cell proliferation. Zbl 0935.92024Anderson, A. R. A.; Chaplain, M. A. J. 33 1998 Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation. Zbl 0988.35082Gourley, S. A.; Chaplain, M. A. J.; Davidson, F. A. 30 2001 A mathematical model of vascular tumour growth and invasion. Zbl 0852.92010Orme, M. E.; Chaplain, M. A. J. 30 1996 Mathematical modelling of cancer cell invasion of tissue. Zbl 1148.92021Ramis-Conde, Ignacio; Chaplain, Mark A. J.; Anderson, Alexander R. A. 28 2008 Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies. Zbl 1080.92050Stéphanou, A.; Mcdougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J. 28 2005 Single-cell-based models in biology and medicine. Zbl 1228.92018Anderson, Alexander R. A. (ed.); Chaplain, Mark A. J. (ed.); Rejniak, Katarzyna (ed.) 27 2007 Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis. Zbl 1130.92036Stéphanou, A.; McDougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J. 27 2006 Travelling fronts in a food-limited population model with time delay. Zbl 1006.35051Gourley, S. A.; Chaplain, M. A. J. 27 2002 Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. Zbl 1405.92085Sturrock, Marc; Terry, Alan J.; Xirodimas, Dimitris P.; Thompson, Alastair M.; Chaplain, Mark A. J. 25 2011 Global stability of a Lotka–Volterra type predator–prey model with stage structure and time delay. Zbl 1056.92063Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 24 2004 Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. Zbl 1048.34119Xu, R.; Chaplain, M. A. J.; Davidson, F. A. 24 2004 Persistence and global stability of a ratio-dependent predator-prey model with stage structure. Zbl 1058.92053Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 23 2004 Periodic solutions for a predator-prey model with Holling-type functional response and time delays. Zbl 1064.34053Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 21 2005 A qualitative analysis of some models of tissue growth. Zbl 0786.92011Britton, N. F.; Chaplain, M. A. J. 21 1993 On immunotherapies and cancer vaccination protocols: a mathematical modelling approach. Zbl 1402.92244Joshi, Badal; Wang, Xueying; Banerjee, Sayanti; Tian, Haiyan; Matzavinos, Anastasios; Chaplain, Mark A. J. 19 2009 A positive splitting method for mixed hyperbolic-parabolic systems. Zbl 0981.65112Gerisch, Alf; Griffiths, David F.; Weiner, Rüdiger; Chaplain, Mark A. J. 19 2001 A mathematical model of the first steps of tumour-related angiogenesis: Capillary sprout formation and secondary branching. Zbl 0849.92009Orme, M. E.; Chaplain, M. A. J. 19 1996 Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory. Zbl 0770.92018Chaplain, M. A. J.; Sleeman, B. D. 17 1993 Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Zbl 1086.92025Gerisch, A.; Chaplain, M. A. J. 16 2006 Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. Zbl 0894.92022Orme, M. E.; Chaplain, M. A. J. 16 1997 Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model. Zbl 1411.92146Powathil, Gibin G.; Gordon, Kirsty E.; Hill, Lydia A.; Chaplain, Mark A. J. 15 2012 Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays. Zbl 1142.35477Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 15 2006 Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response. Zbl 1030.34069Xu, Rui; Chaplain, M. A. J. 15 2002 Permanence and periodicity of a delayed ratio-dependent predator–prey model with stage structure. Zbl 1073.34090Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 14 2005 Periodic solution for a three-species Lotka-Volterra food-chain model with time delays. Zbl 1067.92063Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 14 2004 Modelling aspects of cancer growth: Insight from mathematical and numerical analysis and computational simulation. Zbl 1264.92025Chaplain, Mark A. J. 13 2008 Persistence and stability of a stage-structured predator-prey model with time delays. Zbl 1064.92049Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 13 2004 Global asymptotic stability in \(n\)-species nonautonomous Lotka-Volterra competitive systems with infinite delays. Zbl 1029.34060Xu, Rui; Chaplain, M. A. J.; Chen, Lansun 13 2002 Structured models of cell migration incorporating molecular binding processes. Zbl 1373.35317Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J. 12 2017 A multiscale moving boundary model arising in cancer invasion. Zbl 1302.35379Trucu, Dumitru; Lin, Ping; Chaplain, Mark A. J.; Wang, Yangfan 12 2013 Thermostats for “slow” configurational modes. Zbl 1128.82006Samoletov, Alex A.; Dettmann, Carl P.; Chaplain, Mark A. J. 12 2007 Mathematical modelling of angiogenesis in wound healing: Comparison of theory and experiment. Zbl 0964.92022Byrne, H. M.; Chaplain, M. A. J.; Evans, D. L.; Hopkinson, I. 12 2000 A mathematical analysis of a model for tumour angiogenesis. Zbl 0830.92013Chaplain, M. A. J.; Giles, Susan M.; Sleeman, B. D.; Jarvis, R. J. 12 1995 A multiscale mathematical model of tumour invasive growth. Zbl 1373.92065Peng, Lu; Trucu, Dumitru; Lin, Ping; Thompson, Alastair; Chaplain, Mark A. J. 11 2017 On the stability of homogeneous steady states of a chemotaxis system with logistic growth term. Zbl 1342.35037Chaplain, M. A. J.; Tello, J. I. 11 2016 Selected topics in cancer modeling. Genesis, evolution, immune competition, and therapy. Zbl 1149.92015Bellomo, Nicola (ed.); Chaplain, Mark (ed.); De Angelis, Elena (ed.) 11 2008 Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems. Zbl 1125.92059Pearce, Ian G.; Chaplain, Mark A. J.; Schofield, Pietà G.; Anderson, Alexander R. A.; Hubbard, Stephen F. 11 2007 Computing highly accurate solutions of a tumour angiogenesis model. Zbl 1043.92016Valenciano, J.; Chaplain, M. A. J. 11 2003 A mathematical model of trophoblast invasion. Zbl 0921.92014Byrne, H. M.; Chaplain, M. A. J.; Pettet, G. J.; McElwain, D. L. S. 11 1999 A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature. Zbl 1318.92025McDougall, S. R.; Watson, M. G.; Devlin, A. H.; Mitchell, C. A.; Chaplain, M. A. J. 10 2012 Hopf bifurcation in a gene regulatory network model: molecular movement causes oscillations. Zbl 1326.92019Chaplain, Mark; Ptashnyk, Mariya; Sturrock, Marc 9 2015 Spatio-temporal dynamics of the immune system response to cancer. Zbl 0926.92022Chaplain, M. A. J.; Kuznetsov, V. A.; James, Z. H.; Stepanova, L. A. 9 1998 Necrosis and apoptosis: Distinct cell loss mechanisms in a mathematical model of avascular tumour growth. Zbl 0917.92013Byrne, H. M.; Chaplain, M. A. J. 9 1998 The role of dimerisation and nuclear transport in the Hes1 gene regulatory network. Zbl 1297.92032Sturrock, Marc; Hellander, Andreas; Aldakheel, Sahar; Petzold, Linda; Chaplain, Mark A. J. 8 2014 Spatio-temporal modelling of the p53 – mdm2 oscillatory system. Zbl 1173.35325Gordon, K. E.; van Leeuwen, I. M. M.; Laín, S.; Chaplain, M. A. J. 8 2009 A Lotka–Volterra type food chain model with stage structure and time delays. Zbl 1096.34055Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 8 2006 An explicit subparametric spectral element method of lines applied to a tumour angiogenesis system of partial differential equations. Zbl 1043.92017Valenciano, J.; Chaplain, M. A. J. 8 2004 Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks. Zbl 1013.34074Xu, Rui; Chaplain, M. A. J. 8 2002 Explicit solutions of a simplified model of capillary sprout growth during tumor angiogenesis. Zbl 0852.92009Byrne, H. M.; Chaplain, M. A. J. 8 1996 A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue. Zbl 0737.92007Chaplain, M. A. J.; Stuart, A. M. 8 1991 The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity. Zbl 1397.92343Lorenzi, Tommaso; Venkataraman, Chandrasekhar; Lorz, Alexander; Chaplain, Mark A. J. 7 2018 The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 7 2013 Three-scale convergence for processes in heterogeneous media. Zbl 1252.35038Trucu, D.; Chaplain, M. A. J.; Marciniak-Czochra, A. 7 2012 Global convergence of a reaction-diffusion predator-prey model with stage structure and nonlocal delays. Zbl 1130.35349Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 7 2007 Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays. Zbl 1116.92072Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 7 2004 Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay. Zbl 1008.34065Xu, R.; Davidson, F. A.; Chaplain, M. A. J. 7 2002 A gradient-driven mathematical model of antiangiogenesis. Zbl 0962.92018Anderson, A. R. A.; Chaplain, M. A. J.; García-Reimbert, C.; Vargas, C. A. 7 2000 Travelling waves in a model of species migration. Zbl 0949.92026Feltham, D. L.; Chaplain, M. A. J. 7 2000 Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations. Zbl 0858.92006Gourley, S. A.; Britton, N. F.; Chaplain, M. A. J.; Byrne, H. M. 7 1996 On the concentration profile of a growth inhibitory factor in multicell spheroids. Zbl 0771.92009Chaplain, M. A. J.; Britton, N. F. 7 1993 Multiscale mathematical modelling in biology and medicine. Zbl 1217.92055Chaplain, Mark A. J. 6 2011 A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts. Zbl 1334.92122Stéphanou, A.; Chaplain, M. A. J.; Tracqui, P. 6 2004 An analysis of a mathematical model of trophoblast invasion. Zbl 0979.92017Byrne, H. M.; Chaplain, M. A. J.; Pettet, G. J.; McElwain, D. L. S. 6 2001 A mathematical model for the growth and classification of a solid tumor: A new approach via nonlinear elasticity theory using strain-energy functions. Zbl 0761.92018Chaplain, M. A. J.; Sleeman, B. D. 6 1992 Mathematical modelling of cancer invasion: the multiple roles of TGF-\(\beta\) pathway on tumour proliferation and cell adhesion. Zbl 1375.35564Bitsouni, Vasiliki; Chaplain, Mark A. J.; Eftimie, Raluca 5 2017 Spatio-temporal modelling of the NF-\(\kappa\)B intracellular signalling pathway: the roles of diffusion, active transport, and cell geometry. Zbl 1397.92235Terry, Alan J.; Chaplain, Mark A. J. 5 2011 Oscillations and bistability in the dynamics of cytotoxic reactions mediated by the response of immune cells to solid tumours. Zbl 1148.92019Lejeune, O.; Chaplain, M. A. J.; El Akili, I. 5 2008 Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Zbl 1235.92002Enderling, Heiko; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Rowe, Glenn W. A. 5 2006 A Laguerre - Legendre spectral - element method for the solution of partial differential equations on infinite domains: Application to the diffusion of tumour angiogenesis factors. Zbl 1081.92026Valenciano, J.; Chaplain, M. A. J. 5 2005 Steady-state solutions of a generic model for the formation of capillary networks. Zbl 0964.92023Davidson, F. A.; Anderson, A. R. A.; Chaplain, M. A. J. 5 2000 Modelling the immune response to cancer: an individual-based approach accounting for the difference in movement between inactive and activated T cells. Zbl 1396.92037Macfarlane, Fiona R.; Lorenzi, Tommaso; Chaplain, Mark A. J. 4 2018 Computational modelling of cancer development and growth: modelling at multiple scales and multiscale modelling. Zbl 1394.92065Szymańska, Zuzanna; Cytowski, Maciej; Mitchell, Elaine; Macnamara, Cicely K.; Chaplain, Mark A. J. 4 2018 A continuum mathematical model of the developing murine retinal vasculature. Zbl 1334.92053Aubert, M.; Chaplain, M. A. J.; McDougall, S. R.; Devlin, A.; Mitchell, C. A. 4 2011 A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions. Zbl 1398.92036Stéphanou, Angélique; Mylona, Eleni; Chaplain, Mark; Tracqui, Philippe 4 2008 Global stability of a stage-structured predator-prey model with prey dispersal. Zbl 1080.92069Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 4 2005 Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations. Zbl 1062.92076Schofield, Peter G.; Chaplain, Mark A. J.; Hubbard, Stephen F. 4 2005 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 07263762Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 1 2020 A hybrid multiscale model for cancer invasion of the extracellular matrix. Zbl 1443.92080Sfakianakis, Nikolaos; Madzvamuse, Anotida; Chaplain, Mark A. J. 1 2020 Bridging the gap between individual-based and continuum models of growing cell populations. Zbl 1432.92007Chaplain, Mark A. J.; Lorenzi, Tommaso; Macfarlane, Fiona R. 1 2020 A mathematical framework for modelling the metastatic spread of cancer. Zbl 1415.92099Franssen, Linnea C.; Lorenzi, Tommaso; Burgess, Andrew E. F.; Chaplain, Mark A. J. 3 2019 The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity. Zbl 1397.92343Lorenzi, Tommaso; Venkataraman, Chandrasekhar; Lorz, Alexander; Chaplain, Mark A. J. 7 2018 Modelling the immune response to cancer: an individual-based approach accounting for the difference in movement between inactive and activated T cells. Zbl 1396.92037Macfarlane, Fiona R.; Lorenzi, Tommaso; Chaplain, Mark A. J. 4 2018 Computational modelling of cancer development and growth: modelling at multiple scales and multiscale modelling. Zbl 1394.92065Szymańska, Zuzanna; Cytowski, Maciej; Mitchell, Elaine; Macnamara, Cicely K.; Chaplain, Mark A. J. 4 2018 Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model. Zbl 1390.92066Hodgkinson, Arran; Chaplain, Mark A. J.; Domschke, Pia; Trucu, Dumitru 3 2018 Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion. Zbl 1410.92030Bitsouni, Vasiliki; Trucu, Dumitru; Chaplain, Mark A. J.; Eftimie, Raluca 1 2018 Structured models of cell migration incorporating molecular binding processes. Zbl 1373.35317Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J. 12 2017 A multiscale mathematical model of tumour invasive growth. Zbl 1373.92065Peng, Lu; Trucu, Dumitru; Lin, Ping; Thompson, Alastair; Chaplain, Mark A. J. 11 2017 Mathematical modelling of cancer invasion: the multiple roles of TGF-\(\beta\) pathway on tumour proliferation and cell adhesion. Zbl 1375.35564Bitsouni, Vasiliki; Chaplain, Mark A. J.; Eftimie, Raluca 5 2017 Examining the role of individual movement in promoting coexistence in a spatially explicit prisoner’s dilemma. Zbl 1370.92128Burgess, Andrew E. F.; Lorenzi, Tommaso; Schofield, Pietà G.; Hubbard, Stephen F.; Chaplain, Mark A. J. 2 2017 Spatio-temporal models of synthetic genetic oscillators. Zbl 1362.92021Macnamara, Cicely K.; Chaplain, Mark A. J. 2 2017 On the stability of homogeneous steady states of a chemotaxis system with logistic growth term. Zbl 1342.35037Chaplain, M. A. J.; Tello, J. I. 11 2016 Multiscale computational modelling and analysis of cancer invasion. Zbl 1353.92056Trucu, Dumitru; Domschke, Pia; Gerisch, Alf; Chaplain, Mark A. J. 3 2016 Bystander effects and their implications for clinical radiation therapy: insights from multiscale in silico experiments. Zbl 1343.92130Powathil, Gibin G.; Munro, Alastair J.; Chaplain, Mark A. J.; Swat, Maciej 3 2016 Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model. Zbl 1382.35308Burgess, A. E. F.; Schofield, P. G.; Hubbard, S. F.; Chaplain, M. A. J.; Lorenzi, T. 2 2016 Hopf bifurcation in a gene regulatory network model: molecular movement causes oscillations. Zbl 1326.92019Chaplain, Mark; Ptashnyk, Mariya; Sturrock, Marc 9 2015 Mean field analysis of a spatial stochastic model of a gene regulatory network. Zbl 1350.92020Sturrock, M.; Murray, P. J.; Matzavinos, A.; Chaplain, M. A. J. 2 2015 Mathematical modelling of cancer invasion: implications of cell adhesion variability for tumour infiltrative growth patterns. Zbl 1303.92043Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J. 33 2014 The role of dimerisation and nuclear transport in the Hes1 gene regulatory network. Zbl 1297.92032Sturrock, Marc; Hellander, Andreas; Aldakheel, Sahar; Petzold, Linda; Chaplain, Mark A. J. 8 2014 A multiscale moving boundary model arising in cancer invasion. Zbl 1302.35379Trucu, Dumitru; Lin, Ping; Chaplain, Mark A. J.; Wang, Yangfan 12 2013 The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 7 2013 Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model. Zbl 1411.92146Powathil, Gibin G.; Gordon, Kirsty E.; Hill, Lydia A.; Chaplain, Mark A. J. 15 2012 A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature. Zbl 1318.92025McDougall, S. R.; Watson, M. G.; Devlin, A. H.; Mitchell, C. A.; Chaplain, M. A. J. 10 2012 Three-scale convergence for processes in heterogeneous media. Zbl 1252.35038Trucu, D.; Chaplain, M. A. J.; Marciniak-Czochra, A. 7 2012 Intracellular modelling of cell-matrix adhesion during cancer cell invasion. Zbl 1241.92033Andasari, V.; Chaplain, M. A. J. 3 2012 Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. Zbl 1230.92022Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P.; Chaplain, Mark A. J. 42 2011 Mathematical modelling of cancer invasion: the importance of cell – cell adhesion and cell – matrix adhesion. Zbl 1221.35189Chaplain, Mark A. J.; Lachowicz, Mirosław; Szymańska, Zuzanna; Wrzosek, Dariusz 33 2011 Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. Zbl 1405.92085Sturrock, Marc; Terry, Alan J.; Xirodimas, Dimitris P.; Thompson, Alastair M.; Chaplain, Mark A. J. 25 2011 Multiscale mathematical modelling in biology and medicine. Zbl 1217.92055Chaplain, Mark A. J. 6 2011 Spatio-temporal modelling of the NF-\(\kappa\)B intracellular signalling pathway: the roles of diffusion, active transport, and cell geometry. Zbl 1397.92235Terry, Alan J.; Chaplain, Mark A. J. 5 2011 A continuum mathematical model of the developing murine retinal vasculature. Zbl 1334.92053Aubert, M.; Chaplain, M. A. J.; McDougall, S. R.; Devlin, A.; Mitchell, C. A. 4 2011 Modelling the impact of pericyte migration and coverage of vessels on the efficacy of vascular disrupting agents. Zbl 1190.35219McDougall, S. R.; Chaplain, M. A. J.; Stéphanou, A.; Anderson, A. R. A. 2 2010 Multiscale modelling and nonlinear simulation of vascular tumour growth. Zbl 1311.92040Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 63 2009 Mathematical modelling of cancer invasion of tissue: the role and effect of nonlocal interactions. Zbl 1171.35066Szymańska, Zuzanna; Rodrigo, Cristian Morales; Lachowicz, Mirosław; Chaplain, Mark A. J. 56 2009 On immunotherapies and cancer vaccination protocols: a mathematical modelling approach. Zbl 1402.92244Joshi, Badal; Wang, Xueying; Banerjee, Sayanti; Tian, Haiyan; Matzavinos, Anastasios; Chaplain, Mark A. J. 19 2009 Spatio-temporal modelling of the p53 – mdm2 oscillatory system. Zbl 1173.35325Gordon, K. E.; van Leeuwen, I. M. M.; Laín, S.; Chaplain, M. A. J. 8 2009 Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. Zbl 1397.92326Gerisch, A.; Chaplain, M. A. J. 78 2008 Mathematical modelling of cancer cell invasion of tissue. Zbl 1148.92021Ramis-Conde, Ignacio; Chaplain, Mark A. J.; Anderson, Alexander R. A. 28 2008 Modelling aspects of cancer growth: Insight from mathematical and numerical analysis and computational simulation. Zbl 1264.92025Chaplain, Mark A. J. 13 2008 Selected topics in cancer modeling. Genesis, evolution, immune competition, and therapy. Zbl 1149.92015Bellomo, Nicola (ed.); Chaplain, Mark (ed.); De Angelis, Elena (ed.) 11 2008 Oscillations and bistability in the dynamics of cytotoxic reactions mediated by the response of immune cells to solid tumours. Zbl 1148.92019Lejeune, O.; Chaplain, M. A. J.; El Akili, I. 5 2008 A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions. Zbl 1398.92036Stéphanou, Angélique; Mylona, Eleni; Chaplain, Mark; Tracqui, Philippe 4 2008 Single-cell-based models in biology and medicine. Zbl 1228.92018Anderson, Alexander R. A. (ed.); Chaplain, Mark A. J. (ed.); Rejniak, Katarzyna (ed.) 27 2007 Thermostats for “slow” configurational modes. Zbl 1128.82006Samoletov, Alex A.; Dettmann, Carl P.; Chaplain, Mark A. J. 12 2007 Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems. Zbl 1125.92059Pearce, Ian G.; Chaplain, Mark A. J.; Schofield, Pietà G.; Anderson, Alexander R. A.; Hubbard, Stephen F. 11 2007 Global convergence of a reaction-diffusion predator-prey model with stage structure and nonlocal delays. Zbl 1130.35349Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 7 2007 Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Zbl 1108.92023Chaplain, M. A. J.; Lolas, G. 84 2006 Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Zbl 1098.92037Chaplain, M. A. J.; Graziano, L.; Preziosi, L. 57 2006 Mathematical modelling of the influence of blood rheological properties upon adaptative tumour-induced angiogenesis. Zbl 1130.92036Stéphanou, A.; McDougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J. 27 2006 Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Zbl 1086.92025Gerisch, A.; Chaplain, M. A. J. 16 2006 Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays. Zbl 1142.35477Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 15 2006 A Lotka–Volterra type food chain model with stage structure and time delays. Zbl 1096.34055Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 8 2006 Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Zbl 1235.92002Enderling, Heiko; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Rowe, Glenn W. A. 5 2006 Global convergence of a reaction-diffusion predator-prey model with stage structure for the predator. Zbl 1124.65068Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 1 2006 Mathematical modelling of cancer cell invasion of tissue: the role of the urokinase plasminogen activation system. Zbl 1094.92039Chaplain, M. A. J.; Lolas, G. 115 2005 Mathematical modelling of flow in 2D and 3D vascular networks: Applications to anti-angiogenic and chemotherapeutic drug strategies. Zbl 1080.92050Stéphanou, A.; Mcdougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J. 28 2005 Periodic solutions for a predator-prey model with Holling-type functional response and time delays. Zbl 1064.34053Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 21 2005 Permanence and periodicity of a delayed ratio-dependent predator–prey model with stage structure. Zbl 1073.34090Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 14 2005 A Laguerre - Legendre spectral - element method for the solution of partial differential equations on infinite domains: Application to the diffusion of tumour angiogenesis factors. Zbl 1081.92026Valenciano, J.; Chaplain, M. A. J. 5 2005 Global stability of a stage-structured predator-prey model with prey dispersal. Zbl 1080.92069Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 4 2005 Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations. Zbl 1062.92076Schofield, Peter G.; Chaplain, Mark A. J.; Hubbard, Stephen F. 4 2005 Modelling and analysis of a competitive model with stage structure. Zbl 1066.92058Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 3 2005 Mathematical modelling of the spatio-temporal response of cytotoxic \(T\)-lymphocytes to a solid tumour. Zbl 1061.92038Matzavinos, Anastasios; Chaplain, Mark A. J.; Kuznetsov, Vladimir A. 46 2004 Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments. Zbl 1066.92059Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 33 2004 Global stability of a Lotka–Volterra type predator–prey model with stage structure and time delay. Zbl 1056.92063Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 24 2004 Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. Zbl 1048.34119Xu, R.; Chaplain, M. A. J.; Davidson, F. A. 24 2004 Persistence and global stability of a ratio-dependent predator-prey model with stage structure. Zbl 1058.92053Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 23 2004 Periodic solution for a three-species Lotka-Volterra food-chain model with time delays. Zbl 1067.92063Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 14 2004 Persistence and stability of a stage-structured predator-prey model with time delays. Zbl 1064.92049Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 13 2004 An explicit subparametric spectral element method of lines applied to a tumour angiogenesis system of partial differential equations. Zbl 1043.92017Valenciano, J.; Chaplain, M. A. J. 8 2004 Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays. Zbl 1116.92072Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 7 2004 A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts. Zbl 1334.92122Stéphanou, A.; Chaplain, M. A. J.; Tracqui, P. 6 2004 Periodic solutions of a predator–prey model with stage structure for predator. Zbl 1048.92035Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 4 2004 Persistence and periodicity of a delayed ratio-dependent predator–prey model with stage structure and prey dispersal. Zbl 1056.92062Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 3 2004 Periodic solutions of a delayed predator-prey model with stage structure for predator. Zbl 1086.34058Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 2 2004 Periodic solutions of a discrete time three-species Lotka-Volterra food-chain system. Zbl 1076.39011Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 1 2004 Mathematical modelling of tissue invasion. Zbl 1337.92103Chaplain, Mark A. J.; Anderson, Alexander R. A. 35 2003 Computing highly accurate solutions of a tumour angiogenesis model. Zbl 1043.92016Valenciano, J.; Chaplain, M. A. J. 11 2003 Gobal asymptotic stability in \(n\)-species nonautonomous Lotka-Volterra competitive systems with delays. Zbl 1033.34078Xu, Rui; Chen, Lansun; Chaplain, M. A. J. 3 2003 Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Zbl 1334.92106McDougall, S. R.; Anderson, A. R. A.; Chaplain, M. A. J.; Sherratt, J. A. 47 2002 Travelling fronts in a food-limited population model with time delay. Zbl 1006.35051Gourley, S. A.; Chaplain, M. A. J. 27 2002 Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response. Zbl 1030.34069Xu, Rui; Chaplain, M. A. J. 15 2002 Global asymptotic stability in \(n\)-species nonautonomous Lotka-Volterra competitive systems with infinite delays. Zbl 1029.34060Xu, Rui; Chaplain, M. A. J.; Chen, Lansun 13 2002 Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks. Zbl 1013.34074Xu, Rui; Chaplain, M. A. J. 8 2002 Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay. Zbl 1008.34065Xu, R.; Davidson, F. A.; Chaplain, M. A. J. 7 2002 Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays. Zbl 1043.34088Xu, Rui; Chaplain, M. A. J. 2 2002 A mathematical analysis of a minimal model of nematode migration in soil. Zbl 1099.92070Feltham, D. L.; Chaplain, M. A. J.; Young, I. M.; Crawford, J. W. 1 2002 Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth. Zbl 0988.92003Chaplain, M. A. J.; Ganesh, M.; Graham, I. G. 66 2001 A new mathematical model for avascular tumour growth. Zbl 0990.92021Sherratt, Jonathan A.; Chaplain, Mark A. J. 63 2001 Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation. Zbl 0988.35082Gourley, S. A.; Chaplain, M. A. J.; Davidson, F. A. 30 2001 A positive splitting method for mixed hyperbolic-parabolic systems. Zbl 0981.65112Gerisch, Alf; Griffiths, David F.; Weiner, Rüdiger; Chaplain, Mark A. J. 19 2001 An analysis of a mathematical model of trophoblast invasion. Zbl 0979.92017Byrne, H. M.; Chaplain, M. A. J.; Pettet, G. J.; McElwain, D. L. S. 6 2001 Global asymptotic stability in a nonautonomous \(n\)-species Lotka-Volterra predator-prey system with infinite delays. Zbl 1034.34092Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 3 2001 Mathematical modelling of tumour invasion and metastasis. Zbl 0947.92012Anderson, A. R. A.; Chaplain, M. A. J.; Newman, E. L.; Steele, R. J. C.; Thompson, A. M. 87 2000 Mathematical modelling of angiogenesis in wound healing: Comparison of theory and experiment. Zbl 0964.92022Byrne, H. M.; Chaplain, M. A. J.; Evans, D. L.; Hopkinson, I. 12 2000 A gradient-driven mathematical model of antiangiogenesis. Zbl 0962.92018Anderson, A. R. A.; Chaplain, M. A. J.; García-Reimbert, C.; Vargas, C. A. 7 2000 Travelling waves in a model of species migration. Zbl 0949.92026Feltham, D. L.; Chaplain, M. A. J. 7 2000 ...and 34 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,205 Authors 69 Chaplain, Mark A. J. 44 Byrne, Helen Mary 29 Xu, Shihe 28 Maini, Philip Kumar 24 Friedman, Avner 23 Cui, Shangbin 21 Winkler, Michael 19 Anderson, Alexander R. A. 19 Tao, Youshan 18 Chen, Fengde 18 Preziosi, Luigi 18 Sherratt, Jonathan A. 17 Lowengrub, John Samuel 17 Painter, Kevin J. 16 Lorenzi, Tommaso 14 Bellomo, Nicola 14 Hu, Bei 14 Wu, Junde 13 Gerisch, Alf 13 Hillen, Thomas 13 Madzvamuse, Anotida 13 Mcelwain, D. L. Sean 12 Perthame, Benoît 12 Trucu, Dumitru 12 Wang, Yifu 11 Carrillo de la Plata, José Antonio 10 Bai, Meng 10 Song, Yongli 10 Surulescu, Christina 10 Wang, Zhian 10 Xu, Changjin 9 Cristini, Vittorio 9 Herrero, Miguel Ángel 9 Oden, John Tinsley 9 Simpson, Matthew J. 9 Stéphanou, Angélique 9 Tello, José Ignacio 9 Volpert, Vitaly A. 9 Zhou, Fujun 8 Bellouquid, Abdelghani 8 Chen, Lansun 8 Davidson, Fordyce A. 8 Eftimie, Raluca 8 Gandolfi, Alberto 8 Jin, Chunhua 8 Koleva, Miglena N. 8 Long, Quan 8 Morales-Rodrigo, Cristian 8 Vulkov, Lubin G. 8 Waters, Sarah Louise 8 Xu, Rui 8 Xu, Shixiong 8 Zhang, Fangwei 8 Zheng, Jiashan 7 Cai, Yan 7 Fasano, Antonio 7 Frieboes, Hermann B. 7 Komarova, Natalia L. 7 Landman, Kerry A. 7 Li, Wan-Tong 7 Li, Zhong 7 Mu, Chunlai 7 Ptashnyk, Mariya 7 Sturrock, Marc 7 Szymańska, Zuzanna 7 Wei, Xuemei 7 Zhang, Qingling 6 Alarcón, Tomás 6 Bodnar, Marek 6 Capasso, Vincenzo 6 Dehghan Takht Fooladi, Mehdi 6 Delitala, Marcello 6 Deutsch, Andreas 6 Drasdo, Dirk 6 Escher, Joachim 6 Guo, Qian 6 King, John Robert 6 Lachowicz, Mirosław 6 McDougall, Steven R. 6 Owen, Markus Roger 6 Peng, Yahong 6 Please, Colin P. 6 Sleeman, Brian D. 6 Teng, Zhi-dong 6 Tosin, Andrea 6 Vauchelet, Nicolas 6 Wu, Jie 6 Xu, Yongzhi S. 5 Caraballo Garrido, Tomás 5 Dai, Binxiang 5 d’Onofrio, Alberto 5 Foryś, Urszula 5 Gaffney, Eamonn A. 5 Galiano Casas, Gonzalo 5 Gerlee, Philip 5 Gourley, Stephen A. 5 Hao, Wenrui 5 Hubbard, Stephen F. 5 Kim, Yangjin 5 Ledzewicz, Urszula ...and 2,105 more Authors all top 5 Cited in 195 Serials 142 Journal of Theoretical Biology 82 Bulletin of Mathematical Biology 66 Journal of Mathematical Biology 65 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 62 Applied Mathematics and Computation 59 Nonlinear Analysis. Real World Applications 57 Mathematical and Computer Modelling 50 Mathematical Biosciences 42 Computers & Mathematics with Applications 39 Journal of Differential Equations 37 Journal of Mathematical Analysis and Applications 28 Discrete and Continuous Dynamical Systems. Series B 25 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 25 Applied Mathematics Letters 24 Journal of Computational and Applied Mathematics 19 Applied Mathematical Modelling 18 Chaos, Solitons and Fractals 18 Abstract and Applied Analysis 18 Advances in Difference Equations 15 International Journal of Biomathematics 14 Discrete Dynamics in Nature and Society 13 SIAM Journal on Applied Mathematics 13 Mathematical Modelling of Natural Phenomena 12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 12 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11 Mathematical Methods in the Applied Sciences 11 Computational & Mathematical Methods in Medicine 10 Applied Numerical Mathematics 10 European Journal of Applied Mathematics 10 Discrete and Continuous Dynamical Systems 10 Mathematical Biosciences and Engineering 9 Journal of Applied Mathematics 9 Journal of Biological Dynamics 8 Journal of Computational Physics 8 Physica D 8 Journal of Applied Mathematics and Computing 8 Discrete and Continuous Dynamical Systems. Series S 7 Applicable Analysis 7 Journal of Statistical Physics 7 Nonlinearity 7 SIAM Journal on Mathematical Analysis 7 Nonlinear Dynamics 6 Journal of Scientific Computing 6 Journal of Nonlinear Science 6 Computational and Applied Mathematics 6 Communications in Nonlinear Science and Numerical Simulation 6 Communications on Pure and Applied Analysis 5 Transactions of the American Mathematical Society 5 Numerical Methods for Partial Differential Equations 5 Multiscale Modeling & Simulation 4 Computer Methods in Applied Mechanics and Engineering 4 International Journal of Control 4 Journal of the Franklin Institute 4 Mathematics and Computers in Simulation 4 Applied Mathematics and Mechanics. (English Edition) 4 Acta Applicandae Mathematicae 4 Journal of Dynamics and Differential Equations 4 Interfaces and Free Boundaries 4 Archives of Computational Methods in Engineering 4 Advances in Complex Systems 3 Archive for Rational Mechanics and Analysis 3 Physica A 3 Numerische Mathematik 3 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 3 Japan Journal of Industrial and Applied Mathematics 3 Communications in Partial Differential Equations 3 Advances in Computational Mathematics 3 Mathematical Population Studies 3 Mathematics and Mechanics of Solids 3 Journal of Theoretical Medicine 3 Mathematical and Computer Modelling of Dynamical Systems 3 SIAM Journal on Applied Dynamical Systems 3 Boundary Value Problems 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Acta Mechanica Sinica 3 International Journal of Differential Equations 3 Afrika Matematika 3 International Journal of Applied and Computational Mathematics 2 International Journal of Engineering Science 2 Journal of the Mechanics and Physics of Solids 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Optimization Theory and Applications 2 Quarterly of Applied Mathematics 2 Studies in Applied Mathematics 2 Theoretical Population Biology 2 Chinese Annals of Mathematics. Series B 2 Acta Mathematicae Applicatae Sinica. English Series 2 Applications of Mathematics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Journal on Scientific Computing 2 Applied Mathematics. Series B (English Edition) 2 NoDEA. Nonlinear Differential Equations and Applications 2 Mathematical Problems in Engineering 2 Computing and Visualization in Science 2 Journal of Inequalities and Applications 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 International Journal of Applied Mathematics and Computer Science 2 Journal of Dynamical and Control Systems 2 Journal of Biological Systems 2 The ANZIAM Journal ...and 95 more Serials all top 5 Cited in 36 Fields 1,203 Biology and other natural sciences (92-XX) 745 Partial differential equations (35-XX) 273 Ordinary differential equations (34-XX) 204 Numerical analysis (65-XX) 94 Dynamical systems and ergodic theory (37-XX) 55 Fluid mechanics (76-XX) 55 Systems theory; control (93-XX) 47 Mechanics of deformable solids (74-XX) 39 Probability theory and stochastic processes (60-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 31 Operator theory (47-XX) 29 Statistical mechanics, structure of matter (82-XX) 27 Integral equations (45-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Computer science (68-XX) 12 Difference and functional equations (39-XX) 11 Statistics (62-XX) 9 Classical thermodynamics, heat transfer (80-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 General and overarching topics; collections (00-XX) 5 Mechanics of particles and systems (70-XX) 4 Functional analysis (46-XX) 3 Real functions (26-XX) 3 Differential geometry (53-XX) 3 Quantum theory (81-XX) 2 Optics, electromagnetic theory (78-XX) 2 Mathematics education (97-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Manifolds and cell complexes (57-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline