Edit Profile (opens in new tab) Chaplain, Mark A. J. Compute Distance To: Compute Author ID: chaplain.mark-a-j Published as: Chaplain, M. A. J.; Chaplain, Mark A. J.; Chaplain, Mark; Chaplain, Mark A. more...less Homepage: http://www.mcs.st-andrews.ac.uk/~majc/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef · theses.fr Documents Indexed: 162 Publications since 1990 7 Contributions as Editor Co-Authors: 145 Co-Authors with 165 Joint Publications 3,018 Co-Co-Authors all top 5 Co-Authors 4 single-authored 33 Xu, Rui 27 Davidson, Fordyce A. 19 Anderson, Alexander R. A. 14 Lorenzi, Tommaso 13 Byrne, Helen Mary 9 Gerisch, Alf 9 McDougall, Steven R. 9 Trucu, Dumitru 7 Hubbard, Stephen F. 7 Schofield, Pietà G. 5 Chen, Lansun 5 Matzavinos, Anastasios 5 Stéphanou, Angélique 4 Britton, Nicholas Ferris 4 Domschke, Pia 4 Macfarlane, Fiona R. 4 Maini, Philip Kumar 4 Orme, Michelle E. 4 Sherratt, Jonathan A. 4 Sleeman, Brian David 4 Sturrock, Marc 4 Villa, Chiara 3 Bellomo, Nicola 3 Burgess, Andrew E. F. 3 Enderling, Heiko 3 Feltham, Daniel L. 3 Franssen, Linnea C. 3 Gourley, Stephen A. 3 Lolas, Georgios 3 Lowengrub, John Samuel 3 Macnamara, Cicely K. 3 Powathil, Gibin G. 3 Preziosi, Luigi 3 Szymańska, Zuzanna 3 Thompson, Alastair M. 3 Valenciano, José 2 Andasari, Vivi 2 Bitsouni, Vasiliki 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 Lewis, Mark Alun 2 Lin, Ping 2 Liu, Sijia 2 Lorz, Alexander 2 Marciniak-Czochra, Anna K. 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 Sfakianakis, Nikolaos I. 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 Bonner, John 1 Brezzi, Franco 1 Ciarletta, Pasquale 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 Frieboes, Hermann B. 1 Ganesh, Mahadevan 1 Giles, Susan M. 1 Giverso, Chiara 1 Graham, Ivan G. 1 Graziano, L. 1 Griffiths, David F. 1 Hellander, Andreas 1 Hillen, Thomas 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 ...and 49 more Co-Authors all top 5 Serials 21 Journal of Theoretical Biology 16 Bulletin of Mathematical Biology 13 Journal of Mathematical Biology 12 Applied Mathematics and Computation 12 Mathematical and Computer Modelling 9 Applied Mathematics Letters 9 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 5 Mathematical Modelling of Natural Phenomena 4 Journal of Mathematical Analysis and Applications 4 Mathematical Medicine and Biology 3 Mathematical Biosciences and Engineering 2 Applicable Analysis 2 IMA Journal of Applied Mathematics 2 SIAM Journal on Applied Mathematics 2 Multiscale Modeling & Simulation 1 Computers & Mathematics with Applications 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 Communications on Applied Nonlinear Analysis 1 Differential Equations and Dynamical Systems 1 Vietnam Journal of Mathematics 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 Springer Proceedings in Mathematics & Statistics 1 Modeling and Simulation in Science, Engineering and Technology all top 5 Fields 166 Biology and other natural sciences (92-XX) 77 Partial differential equations (35-XX) 35 Ordinary differential equations (34-XX) 23 Numerical analysis (65-XX) 6 General and overarching topics; collections (00-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Probability theory and stochastic processes (60-XX) 4 Mechanics of deformable solids (74-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 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Integral equations (45-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 Open 149 Publications have been cited 3,246 times in 1,731 Documents Cited by ▼ Year ▼ Continuous and discrete mathematical models of tumor-induced angiogenesis. Zbl 0923.92011Anderson, A. R. A.; Chaplain, M. A. J. 230 1998 Growth of nonnecrotic tumors in the presence and absence of inhibitors. Zbl 0836.92011Byrne, H. M.; Chaplain, M. A. J. 163 1995 Mathematical modelling of cancer cell invasion of tissue: the role of the urokinase plasminogen activation system. Zbl 1094.92039Chaplain, M. A. J.; Lolas, G. 144 2005 Growth of necrotic tumors in the presence and absence of inhibitors. Zbl 0856.92010Byrne, H. M.; Chaplain, M. A. J. 128 1996 Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Zbl 1108.92023Chaplain, M. A. J.; Lolas, G. 114 2006 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. 109 2000 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. 89 2008 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. 80 2001 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. 77 2009 A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor. Zbl 0783.92019Chaplain, M. A. J.; Stuart, A. M. 72 1993 Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development. Zbl 0859.92012Chaplain, M. A. J. 72 1996 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 72 2009 A new mathematical model for avascular tumour growth. Zbl 0990.92021Sherratt, Jonathan A.; Chaplain, Mark A. J. 72 2001 Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Zbl 0883.92014Byrne, H. M.; Chaplain, M. A. J. 69 1996 Free boundary value problems associated with the growth and development of multicellular spheroids. Zbl 0906.92016Byrne, H. M.; Chaplain, M. A. J. 64 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. 63 2006 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. 56 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. 51 2011 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. 48 2002 Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions. Zbl 0812.92011Byrne, H. M.; Chaplain, M. A. J. 45 1995 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 45 2011 Mathematical modelling of tissue invasion. Zbl 1337.92103Chaplain, Mark A. J.; Anderson, Alexander R. A. 44 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. 43 2014 Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation. Zbl 0988.35082Gourley, S. A.; Chaplain, M. A. J.; Davidson, F. A. 41 2001 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. 35 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. 34 1998 Mathematical modelling of cancer cell invasion of tissue. Zbl 1148.92021Ramis-Conde, Ignacio; Chaplain, Mark A. J.; Anderson, Alexander R. A. 32 2008 A mathematical model of vascular tumour growth and invasion. Zbl 0852.92010Orme, M. E.; Chaplain, M. A. J. 32 1996 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. 32 2004 Travelling fronts in a food-limited population model with time delay. Zbl 1006.35051Gourley, S. A.; Chaplain, M. A. J. 32 2002 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. 29 2005 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. 28 2006 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. 28 2009 Single-cell-based models in biology and medicine. Zbl 1228.92018 27 2007 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. 26 2004 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. 25 1996 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. 25 2004 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. 24 2011 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. 23 2005 A positive splitting method for mixed hyperbolic-parabolic systems. Zbl 0981.65112Gerisch, Alf; Griffiths, David F.; Weiner, Rüdiger; Chaplain, Mark A. J. 21 2001 A qualitative analysis of some models of tissue growth. Zbl 0786.92011Britton, N. F.; Chaplain, M. A. J. 21 1993 Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Zbl 1086.92025Gerisch, A.; Chaplain, M. A. J. 21 2006 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 20 2020 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. 19 2012 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. 19 1993 A multiscale mathematical model of tumour invasive growth. Zbl 1373.92065Peng, Lu; Trucu, Dumitru; Lin, Ping; Thompson, Alastair; Chaplain, Mark A. J. 19 2017 Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies. Zbl 0894.92022Orme, M. E.; Chaplain, M. A. J. 17 1997 Structured models of cell migration incorporating molecular binding processes. Zbl 1373.35317Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J. 17 2017 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. 16 2006 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. 16 2004 Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response. Zbl 1030.34069Xu, Rui; Chaplain, M. A. J. 16 2002 A multiscale moving boundary model arising in cancer invasion. Zbl 1302.35379Trucu, Dumitru; Lin, Ping; Chaplain, Mark A. J.; Wang, Yangfan 16 2013 On the stability of homogeneous steady states of a chemotaxis system with logistic growth term. Zbl 1342.35037Chaplain, M. A. J.; Tello, J. I. 16 2016 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. 15 2005 Persistence and stability of a stage-structured predator-prey model with time delays. Zbl 1064.92049Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 15 2004 Modelling aspects of cancer growth: Insight from mathematical and numerical analysis and computational simulation. Zbl 1264.92025Chaplain, Mark A. J. 15 2008 Three-scale convergence for processes in heterogeneous media. Zbl 1252.35038Trucu, D.; Chaplain, M. A. J.; Marciniak-Czochra, A. 15 2012 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. 14 2018 Selected topics in cancer modeling. Genesis, evolution, immune competition, and therapy. Zbl 1149.92015 13 2008 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 Thermostats for “slow” configurational modes. Zbl 1128.82006Samoletov, Alex A.; Dettmann, Carl P.; Chaplain, Mark A. J. 13 2007 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 Hopf bifurcation in a gene regulatory network model: molecular movement causes oscillations. Zbl 1326.92019Chaplain, Mark; Ptashnyk, Mariya; Sturrock, Marc 12 2015 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. 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. 11 2000 Computing highly accurate solutions of a tumour angiogenesis model. Zbl 1043.92016Valenciano, J.; Chaplain, M. A. J. 11 2003 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. 11 2012 A mathematical model of trophoblast invasion. Zbl 0921.92014Byrne, H. M.; Chaplain, M. A. J.; Pettet, G. J.; McElwain, D. L. S. 11 1999 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. 11 1998 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. 10 2019 Necrosis and apoptosis: Distinct cell loss mechanisms in a mathematical model of avascular tumour growth. Zbl 0917.92013Byrne, H. M.; Chaplain, M. A. J. 10 1998 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 10 2017 Bridging the gap between individual-based and continuum models of growing cell populations. Zbl 1432.92007Chaplain, Mark A. J.; Lorenzi, Tommaso; Macfarlane, Fiona R. 9 2020 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. 9 2008 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. 9 2002 On the concentration profile of a growth inhibitory factor in multicell spheroids. Zbl 0771.92009Chaplain, M. A. J.; Britton, N. F. 8 1993 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. 8 1996 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 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 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 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. 8 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. 8 2004 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 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 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 8 2013 Travelling waves in a model of species migration. Zbl 0949.92026Feltham, D. L.; Chaplain, M. A. J. 7 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 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. 7 2001 Explicit solutions of a simplified model of capillary sprout growth during tumor angiogenesis. Zbl 0852.92009Byrne, H. M.; Chaplain, M. A. J. 7 1996 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 hybrid multiscale model for cancer invasion of the extracellular matrix. Zbl 1443.92080Sfakianakis, Nikolaos; Madzvamuse, Anotida; Chaplain, Mark A. J. 7 2020 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. 6 2018 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. 6 2005 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 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 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. 6 2005 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. 6 2018 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 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. 5 2016 Modeling the emergence of phenotypic heterogeneity in vascularized tumors. Zbl 1464.35382Villa, Chiara; Chaplain, Mark A.; Lorenzi, Tommaso 3 2021 Evolutionary dynamics in vascularised tumours under chemotherapy: mathematical modelling, asymptotic analysis and numerical simulations. Zbl 1464.35381Villa, Chiara; Chaplain, Mark A. J.; Lorenzi, Tommaso 1 2021 A novel 3D atomistic-continuum cancer invasion model: in silico simulations of an in vitro organotypic invasion assay. Zbl 1465.92026Franssen, Linnea C.; Sfakianakis, Nikolaos; Chaplain, Mark A. J. 1 2021 Mechanical models of pattern and form in biological tissues: the role of stress-strain constitutive equations. Zbl 1467.92038Villa, Chiara; Chaplain, Mark A. J.; Gerisch, Alf; Lorenzi, Tommaso 1 2021 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 20 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. 9 2020 A hybrid multiscale model for cancer invasion of the extracellular matrix. Zbl 1443.92080Sfakianakis, Nikolaos; Madzvamuse, Anotida; Chaplain, Mark A. J. 7 2020 Discrete and continuum phenotype-structured models for the evolution of cancer cell populations under chemotherapy. Zbl 1467.92101Stace, Rebecca E. A.; Stiehl, Thomas; Chaplain, Mark A. J.; Marciniak-Czochra, Anna; Lorenzi, Tommaso 4 2020 A mathematical multi-organ model for bidirectional epithelial-mesenchymal transitions in the metastatic spread of cancer. Zbl 1457.92076Franssen, Linnea C.; Chaplain, Mark A. J. 1 2020 A hybrid discrete-continuum approach to model Turing pattern formation. Zbl 1468.92020Macfarlane, Fiona R.; Chaplain, Mark A. J.; Lorenzi, Tommaso 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. 10 2019 Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes. Zbl 1428.35619Chaplain, Mark A. J.; Giverso, Chiara; Lorenzi, Tommaso; Preziosi, Luigi 5 2019 A stochastic individual-based model to explore the role of spatial interactions and antigen recognition in the immune response against solid tumours. Zbl 1420.92014Macfarlane, F. R.; Chaplain, M. A. J.; Lorenzi, T. 2 2019 Spatial-stochastic modelling of synthetic gene regulatory networks. Zbl 1411.92121Macnamara, Cicely K.; Mitchell, Elaine I.; Chaplain, Mark A. J. 1 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. 14 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. 6 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. 6 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 4 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 2 2018 A multiscale mathematical model of tumour invasive growth. Zbl 1373.92065Peng, Lu; Trucu, Dumitru; Lin, Ping; Thompson, Alastair; Chaplain, Mark A. J. 19 2017 Structured models of cell migration incorporating molecular binding processes. Zbl 1373.35317Domschke, Pia; Trucu, Dumitru; Gerisch, Alf; Chaplain, Mark A. J. 17 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 10 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. 4 2017 Spatio-temporal models of synthetic genetic oscillators. Zbl 1362.92021Macnamara, Cicely K.; Chaplain, Mark A. J. 3 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. 16 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. 5 2016 Multiscale computational modelling and analysis of cancer invasion. Zbl 1353.92056Trucu, Dumitru; Domschke, Pia; Gerisch, Alf; Chaplain, Mark A. J. 4 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 Hopf bifurcation in a gene regulatory network model: molecular movement causes oscillations. Zbl 1326.92019Chaplain, Mark; Ptashnyk, Mariya; Sturrock, Marc 12 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. 3 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. 43 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 16 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 8 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. 19 2012 Three-scale convergence for processes in heterogeneous media. Zbl 1252.35038Trucu, D.; Chaplain, M. A. J.; Marciniak-Czochra, A. 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. 11 2012 Intracellular modelling of cell-matrix adhesion during cancer cell invasion. Zbl 1241.92033Andasari, V.; Chaplain, M. A. J. 4 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. 51 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 45 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. 24 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. 1 2010 Modelling contact spread of infection in host-parasitoid systems: vertical transmission of pathogens can cause chaos. Zbl 1403.92307Preedy, Katharine F.; Schofield, Pietà G.; Liu, Sijia; Matzavinos, Anastasios; Chaplain, Mark A. J.; Hubbard, Stephen F. 1 2010 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. 77 2009 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 72 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. 28 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. 89 2008 Mathematical modelling of cancer cell invasion of tissue. Zbl 1148.92021Ramis-Conde, Ignacio; Chaplain, Mark A. J.; Anderson, Alexander R. A. 32 2008 Modelling aspects of cancer growth: Insight from mathematical and numerical analysis and computational simulation. Zbl 1264.92025Chaplain, Mark A. J. 15 2008 Selected topics in cancer modeling. Genesis, evolution, immune competition, and therapy. Zbl 1149.92015 13 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. 9 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 1228.92018 27 2007 Thermostats for “slow” configurational modes. Zbl 1128.82006Samoletov, Alex A.; Dettmann, Carl P.; Chaplain, Mark A. J. 13 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. 12 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. 8 2007 A mathematical model of breast cancer development, local treatment and recurrence. Zbl 1451.92091Enderling, Heiko; Chaplain, Mark A. J.; Anderson, Alexander R. A.; Vaidya, Jayant S. 4 2007 Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Zbl 1108.92023Chaplain, M. A. J.; Lolas, G. 114 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. 63 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. 28 2006 Robust numerical methods for taxis-diffusion-reaction systems: applications to biomedical problems. Zbl 1086.92025Gerisch, A.; Chaplain, M. A. J. 21 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. 16 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 Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies. Zbl 1447.92096McDougall, Steven R.; Anderson, Alexander R. A.; Chaplain, Mark A. J. 4 2006 Mathematical modelling of radiotherapy strategies for early breast cancer. Zbl 1447.92195Enderling, Heiko; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Munro, Alastair J.; Vaidya, Jayant S. 2 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 Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications. Zbl 1447.92358Pearce, Ian G.; Chaplain, Mark A. J.; Schofield, Peter G.; Anderson, Alexander R. A.; Hubbard, Stephen F. 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. 144 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. 29 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. 23 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. 15 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. 6 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. 6 2005 Modelling and analysis of a competitive model with stage structure. Zbl 1066.92058Xu, Rui; Chaplain, M. A. J.; Davidson, F. A. 4 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 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. 56 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. 35 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. 32 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. 26 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. 25 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. 16 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. 15 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. 8 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. 4 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. 3 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. 44 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. 48 2002 Travelling fronts in a food-limited population model with time delay. Zbl 1006.35051Gourley, S. A.; Chaplain, M. A. J. 32 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. 16 2002 ...and 49 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,551 Authors 79 Chaplain, Mark A. J. 50 Byrne, Helen Mary 33 Maini, Philip Kumar 33 Xu, Shihe 27 Lorenzi, Tommaso 26 Winkler, Michael 24 Cui, Shangbin 24 Friedman, Avner 24 Tao, Youshan 19 Anderson, Alexander R. A. 19 Chen, Fengde 19 Painter, Kevin J. 19 Preziosi, Luigi 19 Sherratt, Jonathan A. 18 Bellomo, Nicola 18 Lowengrub, John Samuel 17 Simpson, Matthew J. 16 Wu, Junde 15 Gerisch, Alf 15 Hu, Bei 15 Perthame, Benoît 14 Madzvamuse, Anotida 14 Trucu, Dumitru 13 Hillen, Thomas 13 Mcelwain, D. L. Sean 13 Surulescu, Christina 12 Oden, John Tinsley 12 Wang, Yifu 11 Bai, Meng 11 Carrillo de la Plata, José Antonio 11 Eftimie, Raluca 11 Song, Yongli 10 Koleva, Miglena Nikolaeva 10 Volpert, Vitaly A. 10 Vulkov, Lubin G. 10 Xu, Changjin 10 Zhang, Fangwei 9 Cristini, Vittorio 9 Dai, Feng 9 Dehghan Takht Fooladi, Mehdi 9 Herrero, Miguel Ángel 9 Morales-Rodrigo, Cristian 9 Stéphanou, Angélique 9 Wang, Zhian 9 Zhou, Fujun 8 Cai, Yan 8 Chen, Lansun 8 Davidson, Fordyce A. 8 Delitala, Marcello Edoardo 8 Gandolfi, Alberto 8 Long, Quan 8 Mu, Chunlai 8 Sfakianakis, Nikolaos I. 8 Waters, Sarah Louise 8 Wei, Xuemei 8 Xu, Shixiong 8 Zheng, Jiashan 7 Alarcón, Tomás 7 Bellouquid, Abdelghani 7 Capasso, Vincenzo 7 Degond, Pierre 7 Deutsch, Andreas 7 Fasano, Antonio 7 Frieboes, Hermann B. 7 Jin, Chunhua 7 Kolbe, Niklas 7 Komarova, Natalia L. 7 Landman, Kerry A. 7 Li, Wan-Tong 7 Li, Zhong 7 Negreanu, Mihaela 7 Shangerganesh, Lingeshwaran 7 Sturrock, Marc 7 Suárez, Antonio 7 Szymańska, Zuzanna 7 Vauchelet, Nicolas 7 Wang, Zhi Cheng 7 Xu, Rui 7 Xu, Yongzhi S. 7 Zhang, Qingling 7 Zheng, Pan 6 Banerjee, Sandip 6 Bodnar, Marek 6 Cui, Junzhi 6 Dai, Binxiang 6 Dong, Hao 6 Drasdo, Dirk 6 Escher, Joachim 6 Gaffney, Eamonn A. 6 Giverso, Chiara 6 Guo, Qian 6 Han, Bang-Sheng 6 Hao, Wenrui 6 King, John Robert 6 Knopoff, Damian A. 6 Lachowicz, Mirosław 6 Lima, Ernesto A. B. F. 6 Macfarlane, Fiona R. 6 Malinzi, Joseph 6 McDougall, Steven R. ...and 2,451 more Authors all top 5 Cited in 230 Serials 157 Journal of Theoretical Biology 92 Bulletin of Mathematical Biology 84 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 77 Journal of Mathematical Biology 67 Nonlinear Analysis. Real World Applications 65 Applied Mathematics and Computation 57 Mathematical and Computer Modelling 51 Mathematical Biosciences 47 Journal of Mathematical Analysis and Applications 44 Journal of Differential Equations 43 Computers & Mathematics with Applications 36 Discrete and Continuous Dynamical Systems. Series B 32 Applied Mathematics Letters 28 Journal of Computational and Applied Mathematics 28 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 24 Chaos, Solitons and Fractals 22 Applied Mathematical Modelling 22 Advances in Difference Equations 21 Mathematical Biosciences and Engineering 20 ZAMP. 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A. Mathematical, Physical and Engineering Sciences 4 International Journal of Control 4 Numerische Mathematik 4 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 4 Applied Mathematics and Mechanics. (English Edition) 4 Communications in Partial Differential Equations 4 International Journal of Computer Mathematics 4 Electronic Journal of Differential Equations (EJDE) 4 Advances in Computational Mathematics 4 Mathematical and Computer Modelling of Dynamical Systems 4 Journal of Biological Systems 4 Archives of Computational Methods in Engineering 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Advances in Complex Systems 4 Journal of Applied Analysis and Computation 3 Archive for Rational Mechanics and Analysis 3 Journal of Engineering Mathematics 3 Journal of the Mechanics and Physics of Solids 3 Applied Mathematics and Optimization 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Mathematical Population Studies 3 Journal of Theoretical Medicine 3 The ANZIAM Journal 3 Journal of Evolution Equations 3 Acta Mathematica Scientia. Series A. (Chinese Edition) 3 Acta Mechanica Sinica 3 Kinetic and Related Models 3 Afrika Matematika 2 Acta Mechanica 2 Biological Cybernetics 2 International Journal of Engineering Science 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Optimization Theory and Applications 2 Quarterly of Applied Mathematics 2 Ricerche di Matematica ...and 130 more Serials all top 5 Cited in 37 Fields 1,473 Biology and other natural sciences (92-XX) 940 Partial differential equations (35-XX) 316 Ordinary differential equations (34-XX) 253 Numerical analysis (65-XX) 108 Dynamical systems and ergodic theory (37-XX) 66 Fluid mechanics (76-XX) 60 Systems theory; control (93-XX) 59 Mechanics of deformable solids (74-XX) 50 Calculus of variations and optimal control; optimization (49-XX) 47 Probability theory and stochastic processes (60-XX) 42 Statistical mechanics, structure of matter (82-XX) 37 Operator theory (47-XX) 32 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 29 Integral equations (45-XX) 27 Computer science (68-XX) 12 Difference and functional equations (39-XX) 12 Statistics (62-XX) 8 General and overarching topics; collections (00-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Differential geometry (53-XX) 6 Real functions (26-XX) 6 Mechanics of particles and systems (70-XX) 4 Functional analysis (46-XX) 4 Quantum theory (81-XX) 3 Topological groups, Lie groups (22-XX) 3 Manifolds and cell complexes (57-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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