Edit Profile (opens in new tab) Doelman, Arjen Co-Author Distance Author ID: doelman.arjen Published as: Doelman, Arjen; Doelman, A. Documents Indexed: 89 Publications since 1988, including 2 Books and 1 Additional arXiv Preprint 1 Contribution as Editor · 1 Further Contribution Co-Authors: 73 Co-Authors with 83 Joint Publications 1,711 Co-Co-Authors all top 5 Co-Authors 7 single-authored 20 Kaper, Tasso J. 7 Hek, Geertje 7 Rademacher, Jens Diederich Michael 7 van Heijster, Peter 6 Eckhaus, Wiktor 6 Rottschäfer, Vivi 5 Carter, Paul M. 5 Gardner, Robert A. 5 Promislow, Keith Steven 5 Veerman, Frits 5 Zagaris, Antonios 4 Bastiaansen, Robbin 4 Derks, Gianne 4 Holmes, Philip J. 4 Sewalt, Lotte 3 Chirilus-Bruckner, Martina 3 Nishiura, Yasumasa 3 Schielen, Ralph 3 Susanto, Hadi 3 Titi, Edriss Saleh 3 van Harten, Aart 2 de Rijk, Björn 2 de Swart, Huib E. 2 Grasman, Johan 2 Iron, David 2 Knight, Christopher J. K. 2 Maas, Leo R. M. 2 Rietkerk, Max 2 Sandstede, Björn 2 Scheel, Arnd 2 Schneider, Guido 2 Siero, Eric 2 Siteur, Koen 2 Valkhoff, Nienke 2 van der Ploeg, Harmen 2 van der Stelt, Sjors 2 van Gils, Stephan A. 1 Beck, Margaret 1 Bellsky, Thomas 1 Bollerman, Peter 1 Byrnes, Eleanor 1 Chen, Yuan 1 Domokos, Gábor 1 Duistermaat, Johannes Jisse 1 Eppinga, M. B. 1 Eppinga, Maarten 1 Femius Koenderink, A. 1 Fokkink, Robbert Johan 1 Hayrapetyan, Gurgen 1 Holzer, Matt 1 Hulshof, Josephus 1 Iuorio, Annalisa 1 Jaïbi, Olfa 1 Jones, Christopher K. R. T. 1 Kuske, Rachel A. 1 Lilly, Kaitlynn 1 Meijer, Hil G. E. 1 Meron, Ehud 1 Morgan, David S. 1 Obermayer, Erin 1 Peletier, Lambertus Adrianus 1 Pham Thi, N. N. 1 Radboud, Rainer Kaenders 1 Rao, Shreyas 1 Reinders, Marcel J. T. 1 Shen, Jianhe 1 Sommeijer, Ben P. 1 Takáč, Peter 1 Terra, Guido M. 1 Ueda, Kei-ichi 1 Van de Craats, Jan 1 van der Scheer, H. T. 1 van Langevelde, Frank 1 Verhulst, Ferdinand 1 Visser, Timco P. P. 1 Wetton, Brian R. 1 Wiegerinck, Jan J. O. O. 1 Zegeling, Paul Andries 1 Zijlstra, Julia all top 5 Serials 12 Physica D 9 SIAM Journal on Applied Dynamical Systems 8 Journal of Nonlinear Science 7 Nonlinearity 6 SIAM Journal on Applied Mathematics 5 SIAM Journal on Mathematical Analysis 4 Nieuw Archief voor Wiskunde. Vijfde Serie 3 Journal of Dynamics and Differential Equations 2 Archive for Rational Mechanics and Analysis 2 Journal of Fluid Mechanics 2 Indiana University Mathematics Journal 2 Journal of Differential Equations 2 Memoirs of the American Mathematical Society 2 European Journal of Applied Mathematics 2 Methods and Applications of Analysis 2 Chaos 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Applied Scientific Research 1 Biological Cybernetics 1 Mathematical Methods in the Applied Sciences 1 Numerical Functional Analysis and Optimization 1 European Journal of Mechanics. B. Fluids 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 CWI Syllabus 1 Pitman Research Notes in Mathematics Series 1 Discrete and Continuous Dynamical Systems. Series S 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 73 Partial differential equations (35-XX) 35 Ordinary differential equations (34-XX) 30 Biology and other natural sciences (92-XX) 25 Dynamical systems and ergodic theory (37-XX) 11 Fluid mechanics (76-XX) 6 Geophysics (86-XX) 3 Numerical analysis (65-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 75 Publications have been cited 1,326 times in 647 Documents Cited by ▼ Year ▼ Pattern formation in the one-dimensional Gray-Scott model. Zbl 0905.35044 Doelman, Arjen; Kaper, Tasso J.; Zegeling, Paul A. 105 1997 Large stable pulse solutions in reaction-diffusion equations. Zbl 0994.35058 Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. 91 2001 Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach. Zbl 0943.34039 Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. 81 1998 The dynamics of modulated wave trains. Zbl 1179.35005 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 72 2009 Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model. Zbl 1270.35093 van der Stelt, Sjors; Doelman, Arjen; Hek, Geertje; Rademacher, Jens D. M. 51 2013 A stability index analysis of 1-D patterns of the Gray-Scott model. Zbl 0994.35059 Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. 43 2002 Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes. Zbl 1374.92167 Siero, E.; Doelman, A.; Eppinga, M. B.; Rademacher, J. D. M.; Rietkerk, M.; Siteur, K. 41 2015 Propagation of hexagonal patterns near onset. Zbl 1044.37049 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 38 2003 Pulse dynamics in a three-component system: Existence analysis. Zbl 1173.35068 Doelman, Arjen; van Heijster, Peter; Kaper, Tasso J. 38 2009 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517 Doelman, Arjen; Kaper, Tasso J. 32 2003 Homoclinic stripe patterns. Zbl 1004.35063 Doelman, Arjen; van der Ploeg, Harmen 31 2002 Periodic and quasi-periodic solutions of degenerate modulation equations. Zbl 0744.35058 Doelman, Arjen; Eckhaus, Wiktor 30 1991 Front interactions in a three-component system. Zbl 1197.35047 van Heijster, P.; Doelman, A.; Kaper, T. J.; Promislow, K. 28 2010 Pulse dynamics in a three-component system: Stability and bifurcations. Zbl 1153.37437 van Heijster, Peter; Doelman, Arjen; Kaper, Tasso J. 27 2008 Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. Zbl 0979.35074 Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J. 26 2000 Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation. Zbl 0792.35096 Doelman, Arjen; Titi, Edriss S. 26 1993 Nonlinear asymptotic stability of the semistrong pulse dynamics in a regularized Gierer-Meinhardt model. Zbl 1131.35084 Doelman, Arjen; Kaper, Tasso J.; Promislow, Keith 26 2007 Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation. Zbl 1006.92008 Doelman, Arjen; Kaper, Tasso J.; van der Ploeg, Harmen 25 2001 Slowly modulated two-pulse solutions in the Gray–Scott model. II: Geometric theory, bifurcations, and splitting dynamics. Zbl 0989.35073 Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J. 24 2001 An explicit theory for pulses in two component, singularly perturbed, reaction-diffusion equations. Zbl 1339.35021 Doelman, Arjen; Veerman, Frits 24 2015 Meander and pearling of single-curvature bilayer interfaces in the functionalized Cahn-Hilliard equation. Zbl 1316.35026 Doelman, Arjen; Hayrapetyan, Gurgen; Promislow, Keith; Wetton, Brian 23 2014 Spatially periodic multipulse patterns in a generalized Klausmeier-Gray-Scott model. Zbl 1369.34067 Sewalt, Lotte; Doelman, Arjen 23 2017 Traveling waves in the complex Ginzburg-Landau equation. Zbl 0805.35050 Doelman, A. 21 1993 Pinned fronts in heterogeneous media of jump type. Zbl 1208.35010 van Heijster, Peter; Doelman, Arjen; Kaper, Tasso J.; Nishiura, Yasumasa; Ueda, Kei-Ichi 19 2011 Slow time-periodic solutions of the Ginzburg-Landau equation. Zbl 0702.35206 Doelman, Arjen 19 1989 Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation. Zbl 0849.35014 Takáč, P.; Bollerman, P.; Doelman, A.; van Harten, A.; Titi, E. S. 17 1996 Spectra and stability of spatially periodic pulse patterns: Evans function factorization via Riccati transformation. Zbl 1336.35042 de Rijk, Björn; Doelman, Arjen; Rademacher, Jens 15 2016 Pulses in a Gierer-Meinhardt equation with a slow nonlinearity. Zbl 1282.35049 Veerman, Frits; Doelman, Arjen 15 2013 Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems. Zbl 1419.35104 Bastiaansen, Robbin; Carter, Paul; Doelman, Arjen 15 2019 Hopf dances near the tips of Busse balloons. Zbl 1252.35032 Doelman, Arjen; Rademacher, Jens D. M.; van der Stelt, Sjors 14 2012 Climate change, desertification and billiards. Zbl 1301.86005 Doelman, Arjen; Rademacher, Jens; Siero, Eric; Eppinga, Maarten; Rietkerk, Max; Siteur, Koen; Hek, Geertje 14 2013 Existence and stability of traveling pulses in a reaction-diffusion-mechanics system. Zbl 1278.35045 Holzer, Matt; Doelman, Arjen; Kaper, Tasso J. 14 2013 On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation. Zbl 1194.76055 Rottschäfer, Vivi; Doelman, Arjen 13 1998 Finite-dimensional models of the Ginzburg-Landau equation. Zbl 0841.35007 Doelman, Arjen 12 1991 Butterfly catastrophe for fronts in a three-component reaction-diffusion system. Zbl 1325.35088 Chirilus-Bruckner, Martina; Doelman, Arjen; van Heijster, Peter; Rademacher, Jens D. M. 12 2015 Breaking the hidden symmetry in the Ginzburg-Landau equation. Zbl 1194.35406 Doelman, Arjen 12 1996 Pinned fluxons in a Josephson junction with a finite-length inhomogeneity. Zbl 1245.82086 Derks, Gianne; Doelman, Arjen; Knight, Christopher J. K.; Susanto, Hadi 10 2012 Blooming in a nonlocal, coupled phytoplankton-nutrient model. Zbl 1178.35041 Zagaris, A.; Doelman, A.; Thi, N. N. Pham; Sommeijer, B. P. 10 2009 Homoclinic explosions and implosions. Zbl 0881.58044 Doelman, Arjen; Holmes, Philip 10 1996 Adiabatic stability under semi-strong interactions: the weakly damped regime. Zbl 1302.35029 Bellsky, Thomas; Doelman, Arjen; Kaper, Tasso J.; Promislow, Keith 10 2013 The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space. Zbl 1448.34096 Bastiaansen, Robbin; Doelman, Arjen 10 2019 Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model. Zbl 1233.35031 Zagaris, A.; Doelman, A. 9 2011 Destabilization of fronts in a class of bistable systems. Zbl 1063.35023 Doelman, Arjen; Iron, David; Nishiura, Yasumasa 9 2004 Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneity. Zbl 1259.35029 Knight, Christopher J. K.; Derks, Gianne; Doelman, Arjen; Susanto, Hadi 9 2013 Algebraically decaying pulses in a Ginzburg-Landau system with a neutrally stable mode. Zbl 1129.35015 Doelman, Arjen; Hek, Geertje; Valkhoff, Nienke 8 2007 Instability of quasiperiodic solutions of the Ginzburg-Landau equation. Zbl 0840.35104 Doelman, A.; Gardner, R. A.; Jones, C. K. R. T. 8 1995 Stationary periodic patterns in the 1D Gray-Scott model. Zbl 0996.92041 Morgan, David S.; Doelman, Arjen; Kaper, Tasso J. 8 2000 Travelling waves in a singularly perturbed sine-Gordon equation. Zbl 1040.35093 Derks, Gianne; Doelman, Arjen; van Gils, Stephan A.; Visser, Timco 8 2003 Traveling stripes in the Klausmeier model of vegetation pattern formation. Zbl 1403.35132 Carter, Paul; Doelman, Arjen 8 2018 Stabilization by slow diffusion in a real Ginzburg-Landau system. Zbl 1136.37356 Doelman, A.; Hek, G.; Valkhoff, N. 7 2004 Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms. Zbl 0885.58075 Doelman, A.; Rottschäfer, V. 7 1997 A geometric approach to stationary defect solutions in one space dimension. Zbl 1343.34041 Doelman, A.; van Heijster, P.; Xie, F. 7 2016 The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation. Zbl 1485.92177 Jaïbi, Olfa; Doelman, Arjen; Chirilus-Bruckner, Martina; Meron, Ehud 7 2020 Homoclinic bifurcations at the onset of pulse self-replication. Zbl 1217.34074 Doelman, Arjen; Kaper, Tasso J.; Peletier, Lambertus A. 6 2006 Stability analysis of \(\pi\)-Kinks in a \(0-\pi\) Josephson junction. Zbl 1210.39014 Derks, G.; Doelman, A.; Van Gils, S. A.; Susanto, H. 5 2007 On the nonlinear dynamics of free bars in straight channels. Zbl 0789.76040 Schielen, R.; Doelman, A.; de Swart, H. E. 5 1993 Tracking pattern evolution through extended center manifold reduction and singular perturbations. Zbl 1364.35040 Sewalt, L.; Doelman, A.; Meijer, H. G. E.; Rottschäfer, V.; Zagaris, A. 5 2015 Pulse solutions for an extended Klausmeier model with spatially varying coefficients. Zbl 1431.35071 Bastiaansen, Robbin; Chirilus-Bruckner, Martina; Doelman, Arjen 5 2020 Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow. Zbl 0930.37026 Hek, Geertje; Doelman, Arjen; Holmes, Philip 4 1998 A geometric construction of traveling waves in a bioremediation model. Zbl 1100.92060 Beck, M.; Doelman, A.; Kaper, T. J. 4 2006 Destabilization mechanisms of periodic pulse patterns near a homoclinic limit. Zbl 1400.35164 Doelman, Arjen; Rademacher, Jens; de Rijk, Björn; Veerman, Frits 4 2018 Homoclinic saddle-node bifurcations in singularly perturbed systems. Zbl 0949.34031 Doelman, Arjen; Hek, Geertje 3 2000 Homoclinic orbits and chaos in three- and four-dimensional flows. Zbl 1004.37013 Holmes, Philip; Doelman, Arjen; Hek, Geertje; Domokos, Gábor 3 2001 Bifurcations of strongly nonlinear self-excited oscillations. Zbl 0792.34037 Doelman, Arjen; Verhulst, Ferdinand 3 1994 Pulse dynamics in reaction-diffusion equations with strong spatially localized impurities. Zbl 1402.35138 Doelman, Arjen; van Heijster, Peter; Shen, Jianhe 3 2018 Nonlinear dynamics and pattern formation in the natural environment. Proceedings of the international conference held in Noordwijkerhout, The Netherlands, July 4-7, 1994. Zbl 0828.00036 2 1995 Quasi-periodically forced nonlinear Helmholtz oscillators. Zbl 0993.86001 Doelman, Arjen; Femius Koenderink, A.; Maas, Leo R. M. 2 2002 Exponential convergence of the Galerkin approximation for the Ginzburg- Landau equation. Zbl 0806.65088 Doelman, Arjen; Titi, Edriss S. 2 1993 Slow localized patterns in singularly perturbed two-component reaction-diffusion equations. Zbl 1492.35019 Doelman, Arjen 2 2022 Multibump patterns near a co-dimension 2 point. Zbl 0913.35064 Doelman, Arjen; Rottschäfer, Vivi 1 1998 Modulation equations for spatially periodic systems: Derivation and solutions. Zbl 0908.35009 Schielen, R.; Doelman, A. 1 1998 The effect of slow spatial processes on emerging spatiotemporal patterns. Zbl 1374.92163 Doelman, A.; Sewalt, L.; Zagaris, A. 1 2015 Large amplitude radially symmetric spots and gaps in a dryland ecosystem model. Zbl 1526.35025 Byrnes, Eleanor; Carter, Paul; Doelman, Arjen; Liu, Lily 1 2023 Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction-diffusion equations. Zbl 1505.35020 Carter, Paul; Doelman, Arjen; Lilly, Kaitlynn; Obermayer, Erin; Rao, Shreyas 1 2023 Modeling honey bee colonies in winter using a Keller-Segel model with a sign-changing chemotactic coefficient. Zbl 1439.35258 Bastiaansen, Robbin; Doelman, Arjen; van Langevelde, Frank; Rottschäfer, Vivi 1 2020 Large amplitude radially symmetric spots and gaps in a dryland ecosystem model. Zbl 1526.35025 Byrnes, Eleanor; Carter, Paul; Doelman, Arjen; Liu, Lily 1 2023 Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction-diffusion equations. Zbl 1505.35020 Carter, Paul; Doelman, Arjen; Lilly, Kaitlynn; Obermayer, Erin; Rao, Shreyas 1 2023 Slow localized patterns in singularly perturbed two-component reaction-diffusion equations. Zbl 1492.35019 Doelman, Arjen 2 2022 The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation. Zbl 1485.92177 Jaïbi, Olfa; Doelman, Arjen; Chirilus-Bruckner, Martina; Meron, Ehud 7 2020 Pulse solutions for an extended Klausmeier model with spatially varying coefficients. Zbl 1431.35071 Bastiaansen, Robbin; Chirilus-Bruckner, Martina; Doelman, Arjen 5 2020 Modeling honey bee colonies in winter using a Keller-Segel model with a sign-changing chemotactic coefficient. Zbl 1439.35258 Bastiaansen, Robbin; Doelman, Arjen; van Langevelde, Frank; Rottschäfer, Vivi 1 2020 Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems. Zbl 1419.35104 Bastiaansen, Robbin; Carter, Paul; Doelman, Arjen 15 2019 The dynamics of disappearing pulses in a singularly perturbed reaction-diffusion system with parameters that vary in time and space. Zbl 1448.34096 Bastiaansen, Robbin; Doelman, Arjen 10 2019 Traveling stripes in the Klausmeier model of vegetation pattern formation. Zbl 1403.35132 Carter, Paul; Doelman, Arjen 8 2018 Destabilization mechanisms of periodic pulse patterns near a homoclinic limit. Zbl 1400.35164 Doelman, Arjen; Rademacher, Jens; de Rijk, Björn; Veerman, Frits 4 2018 Pulse dynamics in reaction-diffusion equations with strong spatially localized impurities. Zbl 1402.35138 Doelman, Arjen; van Heijster, Peter; Shen, Jianhe 3 2018 Spatially periodic multipulse patterns in a generalized Klausmeier-Gray-Scott model. Zbl 1369.34067 Sewalt, Lotte; Doelman, Arjen 23 2017 Spectra and stability of spatially periodic pulse patterns: Evans function factorization via Riccati transformation. Zbl 1336.35042 de Rijk, Björn; Doelman, Arjen; Rademacher, Jens 15 2016 A geometric approach to stationary defect solutions in one space dimension. Zbl 1343.34041 Doelman, A.; van Heijster, P.; Xie, F. 7 2016 Striped pattern selection by advective reaction-diffusion systems: resilience of banded vegetation on slopes. Zbl 1374.92167 Siero, E.; Doelman, A.; Eppinga, M. B.; Rademacher, J. D. M.; Rietkerk, M.; Siteur, K. 41 2015 An explicit theory for pulses in two component, singularly perturbed, reaction-diffusion equations. Zbl 1339.35021 Doelman, Arjen; Veerman, Frits 24 2015 Butterfly catastrophe for fronts in a three-component reaction-diffusion system. Zbl 1325.35088 Chirilus-Bruckner, Martina; Doelman, Arjen; van Heijster, Peter; Rademacher, Jens D. M. 12 2015 Tracking pattern evolution through extended center manifold reduction and singular perturbations. Zbl 1364.35040 Sewalt, L.; Doelman, A.; Meijer, H. G. E.; Rottschäfer, V.; Zagaris, A. 5 2015 The effect of slow spatial processes on emerging spatiotemporal patterns. Zbl 1374.92163 Doelman, A.; Sewalt, L.; Zagaris, A. 1 2015 Meander and pearling of single-curvature bilayer interfaces in the functionalized Cahn-Hilliard equation. Zbl 1316.35026 Doelman, Arjen; Hayrapetyan, Gurgen; Promislow, Keith; Wetton, Brian 23 2014 Rise and fall of periodic patterns for a generalized Klausmeier-Gray-Scott model. Zbl 1270.35093 van der Stelt, Sjors; Doelman, Arjen; Hek, Geertje; Rademacher, Jens D. M. 51 2013 Pulses in a Gierer-Meinhardt equation with a slow nonlinearity. Zbl 1282.35049 Veerman, Frits; Doelman, Arjen 15 2013 Climate change, desertification and billiards. Zbl 1301.86005 Doelman, Arjen; Rademacher, Jens; Siero, Eric; Eppinga, Maarten; Rietkerk, Max; Siteur, Koen; Hek, Geertje 14 2013 Existence and stability of traveling pulses in a reaction-diffusion-mechanics system. Zbl 1278.35045 Holzer, Matt; Doelman, Arjen; Kaper, Tasso J. 14 2013 Adiabatic stability under semi-strong interactions: the weakly damped regime. Zbl 1302.35029 Bellsky, Thomas; Doelman, Arjen; Kaper, Tasso J.; Promislow, Keith 10 2013 Stability of stationary fronts in a non-linear wave equation with spatial inhomogeneity. Zbl 1259.35029 Knight, Christopher J. K.; Derks, Gianne; Doelman, Arjen; Susanto, Hadi 9 2013 Hopf dances near the tips of Busse balloons. Zbl 1252.35032 Doelman, Arjen; Rademacher, Jens D. M.; van der Stelt, Sjors 14 2012 Pinned fluxons in a Josephson junction with a finite-length inhomogeneity. Zbl 1245.82086 Derks, Gianne; Doelman, Arjen; Knight, Christopher J. K.; Susanto, Hadi 10 2012 Pinned fronts in heterogeneous media of jump type. Zbl 1208.35010 van Heijster, Peter; Doelman, Arjen; Kaper, Tasso J.; Nishiura, Yasumasa; Ueda, Kei-Ichi 19 2011 Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model. Zbl 1233.35031 Zagaris, A.; Doelman, A. 9 2011 Front interactions in a three-component system. Zbl 1197.35047 van Heijster, P.; Doelman, A.; Kaper, T. J.; Promislow, K. 28 2010 The dynamics of modulated wave trains. Zbl 1179.35005 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 72 2009 Pulse dynamics in a three-component system: Existence analysis. Zbl 1173.35068 Doelman, Arjen; van Heijster, Peter; Kaper, Tasso J. 38 2009 Blooming in a nonlocal, coupled phytoplankton-nutrient model. Zbl 1178.35041 Zagaris, A.; Doelman, A.; Thi, N. N. Pham; Sommeijer, B. P. 10 2009 Pulse dynamics in a three-component system: Stability and bifurcations. Zbl 1153.37437 van Heijster, Peter; Doelman, Arjen; Kaper, Tasso J. 27 2008 Nonlinear asymptotic stability of the semistrong pulse dynamics in a regularized Gierer-Meinhardt model. Zbl 1131.35084 Doelman, Arjen; Kaper, Tasso J.; Promislow, Keith 26 2007 Algebraically decaying pulses in a Ginzburg-Landau system with a neutrally stable mode. Zbl 1129.35015 Doelman, Arjen; Hek, Geertje; Valkhoff, Nienke 8 2007 Stability analysis of \(\pi\)-Kinks in a \(0-\pi\) Josephson junction. Zbl 1210.39014 Derks, G.; Doelman, A.; Van Gils, S. A.; Susanto, H. 5 2007 Homoclinic bifurcations at the onset of pulse self-replication. Zbl 1217.34074 Doelman, Arjen; Kaper, Tasso J.; Peletier, Lambertus A. 6 2006 A geometric construction of traveling waves in a bioremediation model. Zbl 1100.92060 Beck, M.; Doelman, A.; Kaper, T. J. 4 2006 Destabilization of fronts in a class of bistable systems. Zbl 1063.35023 Doelman, Arjen; Iron, David; Nishiura, Yasumasa 9 2004 Stabilization by slow diffusion in a real Ginzburg-Landau system. Zbl 1136.37356 Doelman, A.; Hek, G.; Valkhoff, N. 7 2004 Propagation of hexagonal patterns near onset. Zbl 1044.37049 Doelman, Arjen; Sandstede, Björn; Scheel, Arnd; Schneider, Guido 38 2003 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517 Doelman, Arjen; Kaper, Tasso J. 32 2003 Travelling waves in a singularly perturbed sine-Gordon equation. Zbl 1040.35093 Derks, Gianne; Doelman, Arjen; van Gils, Stephan A.; Visser, Timco 8 2003 A stability index analysis of 1-D patterns of the Gray-Scott model. Zbl 0994.35059 Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. 43 2002 Homoclinic stripe patterns. Zbl 1004.35063 Doelman, Arjen; van der Ploeg, Harmen 31 2002 Quasi-periodically forced nonlinear Helmholtz oscillators. Zbl 0993.86001 Doelman, Arjen; Femius Koenderink, A.; Maas, Leo R. M. 2 2002 Large stable pulse solutions in reaction-diffusion equations. Zbl 0994.35058 Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. 91 2001 Spatially periodic and aperiodic multi-pulse patterns in the one-dimensional Gierer-Meinhardt equation. Zbl 1006.92008 Doelman, Arjen; Kaper, Tasso J.; van der Ploeg, Harmen 25 2001 Slowly modulated two-pulse solutions in the Gray–Scott model. II: Geometric theory, bifurcations, and splitting dynamics. Zbl 0989.35073 Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J. 24 2001 Homoclinic orbits and chaos in three- and four-dimensional flows. Zbl 1004.37013 Holmes, Philip; Doelman, Arjen; Hek, Geertje; Domokos, Gábor 3 2001 Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. Zbl 0979.35074 Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J. 26 2000 Stationary periodic patterns in the 1D Gray-Scott model. Zbl 0996.92041 Morgan, David S.; Doelman, Arjen; Kaper, Tasso J. 8 2000 Homoclinic saddle-node bifurcations in singularly perturbed systems. Zbl 0949.34031 Doelman, Arjen; Hek, Geertje 3 2000 Stability analysis of singular patterns in the 1D Gray-Scott model: a matched asymptotics approach. Zbl 0943.34039 Doelman, Arjen; Gardner, Robert A.; Kaper, Tasso J. 81 1998 On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation. Zbl 1194.76055 Rottschäfer, Vivi; Doelman, Arjen 13 1998 Homoclinic saddle-node bifurcations and subshifts in a three-dimensional flow. Zbl 0930.37026 Hek, Geertje; Doelman, Arjen; Holmes, Philip 4 1998 Multibump patterns near a co-dimension 2 point. Zbl 0913.35064 Doelman, Arjen; Rottschäfer, Vivi 1 1998 Modulation equations for spatially periodic systems: Derivation and solutions. Zbl 0908.35009 Schielen, R.; Doelman, A. 1 1998 Pattern formation in the one-dimensional Gray-Scott model. Zbl 0905.35044 Doelman, Arjen; Kaper, Tasso J.; Zegeling, Paul A. 105 1997 Singularly perturbed and nonlocal modulation equations for systems with interacting instability mechanisms. Zbl 0885.58075 Doelman, A.; Rottschäfer, V. 7 1997 Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation. Zbl 0849.35014 Takáč, P.; Bollerman, P.; Doelman, A.; van Harten, A.; Titi, E. S. 17 1996 Breaking the hidden symmetry in the Ginzburg-Landau equation. Zbl 1194.35406 Doelman, Arjen 12 1996 Homoclinic explosions and implosions. Zbl 0881.58044 Doelman, Arjen; Holmes, Philip 10 1996 Instability of quasiperiodic solutions of the Ginzburg-Landau equation. Zbl 0840.35104 Doelman, A.; Gardner, R. A.; Jones, C. K. R. T. 8 1995 Nonlinear dynamics and pattern formation in the natural environment. Proceedings of the international conference held in Noordwijkerhout, The Netherlands, July 4-7, 1994. Zbl 0828.00036 2 1995 Bifurcations of strongly nonlinear self-excited oscillations. Zbl 0792.34037 Doelman, Arjen; Verhulst, Ferdinand 3 1994 Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation. Zbl 0792.35096 Doelman, Arjen; Titi, Edriss S. 26 1993 Traveling waves in the complex Ginzburg-Landau equation. Zbl 0805.35050 Doelman, A. 21 1993 On the nonlinear dynamics of free bars in straight channels. Zbl 0789.76040 Schielen, R.; Doelman, A.; de Swart, H. E. 5 1993 Exponential convergence of the Galerkin approximation for the Ginzburg- Landau equation. Zbl 0806.65088 Doelman, Arjen; Titi, Edriss S. 2 1993 Periodic and quasi-periodic solutions of degenerate modulation equations. Zbl 0744.35058 Doelman, Arjen; Eckhaus, Wiktor 30 1991 Finite-dimensional models of the Ginzburg-Landau equation. Zbl 0841.35007 Doelman, Arjen 12 1991 Slow time-periodic solutions of the Ginzburg-Landau equation. Zbl 0702.35206 Doelman, Arjen 19 1989 all cited Publications top 5 cited Publications all top 5 Cited by 838 Authors 50 Wei, Juncheng 38 Ward, Michael J. 35 Doelman, Arjen 26 Kolokolnikov, Theodore 20 Scheel, Arnd 18 van Heijster, Peter 18 Winter, Matthias 13 Promislow, Keith Steven 13 Sandstede, Björn 13 Schneider, Guido 12 Nishiura, Yasumasa 12 Sherratt, Jonathan A. 12 Tzou, Justin C. 11 Rademacher, Jens Diederich Michael 10 Chen, Chaonien 10 de Rijk, Björn 9 Choi, Yung-Sze 9 Johnson, Mathew A. 9 Shi, Junping 9 Zumbrun, Kevin R. 8 Choudhury, Sudipto Roy 8 Lloyd, David J. B. 8 Rodrigues, Luis Miguel 8 Titi, Edriss Saleh 7 Champneys, Alan R. 7 Derks, Gianne 7 Duan, Jinqiao 7 Iron, David 7 Kaper, Tasso J. 7 Mancas, Stefan C. 7 Noble, Pascal 7 Teramoto, Takashi 6 Carter, Paul M. 6 Ei, Shin-Ichiro 6 Gómez, Daniel Armando 6 Haragus, Mariana 6 Hupkes, Hermen Jan 6 Jones, Christopher K. R. T. 6 Mielke, Alexander 6 Rottschäfer, Vivi 6 Wise, Steven M. 6 You, Yuncheng 5 Beck, Margaret 5 Chirilus-Bruckner, Martina 5 Düll, Wolf-Patrick 5 Eigentler, Lukas 5 Jung, Soyeun 5 Kapitula, Todd M. 5 Marangell, Robert 5 Palencia, José Luis Díaz 5 Shen, Jianhe 5 Sun, Guiquan 5 Uecker, Hannes 5 Wechselberger, Martin 5 Zhou, Jun 4 Avery, Montie 4 Bastiaansen, Robbin 4 Breña-Medina, Víctor F. 4 Bridges, Thomas J. 4 Du, Zengji 4 Gai, Chunyi 4 Gandhi, Punit 4 Goh, Ryan N. 4 Hek, Geertje 4 Hou, Xiaojie 4 Jaramillo, Gabriela 4 Knobloch, Edgar 4 Latushkin, Yuri 4 Siero, Eric 4 Tse, Wang Hung 4 Veerman, Frits 4 Wang, Cheng 4 Xie, Shuangquan 4 Zegeling, Paul Andries 4 Zhang, Guohong 4 Zhang, Jimin 3 Ao, Weiwei 3 Avitabile, Daniele 3 Barker, Blake 3 Biswas, Animikh 3 Chen, Shuang 3 Chen, Yuan 3 Choi, Yuncherl 3 Consolo, Giancarlo 3 Dai, Shibin 3 Ekomasov, Evgeniĭ Grigor’evich 3 Feng, Wenqiang 3 Gallay, Thierry 3 Grifó, Gabriele 3 Grujić, Zoran 3 Ha, Taeyoung 3 Holzer, Matt 3 Khaliq, Abdul Q. M. 3 Kozyreff, Gregory 3 Krause, Andrew L. 3 Kukavica, Igor 3 Li, Li 3 Li, You 3 Lowengrub, John Samuel 3 Maini, Philip Kumar ...and 738 more Authors all top 5 Cited in 138 Serials 78 Physica D 46 Journal of Differential Equations 31 SIAM Journal on Applied Dynamical Systems 24 Journal of Dynamics and Differential Equations 22 Journal of Nonlinear Science 20 Nonlinearity 18 European Journal of Applied Mathematics 16 Journal of Mathematical Biology 13 SIAM Journal on Mathematical Analysis 13 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 12 Journal of Mathematical Analysis and Applications 12 Chaos 12 Discrete and Continuous Dynamical Systems. Series B 11 Chaos, Solitons and Fractals 11 Applied Mathematics and Computation 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 SIAM Journal on Applied Mathematics 9 Archive for Rational Mechanics and Analysis 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Discrete and Continuous Dynamical Systems. Series S 8 Computers & Mathematics with Applications 7 Bulletin of Mathematical Biology 7 Journal of Computational and Applied Mathematics 7 Studies in Applied Mathematics 7 Nonlinear Analysis. Real World Applications 6 Journal of Computational Physics 6 Journal of Mathematical Physics 6 Applied Mathematics Letters 6 Japan Journal of Industrial and Applied Mathematics 5 Communications in Mathematical Physics 5 Journal of Fluid Mechanics 5 Communications in Nonlinear Science and Numerical Simulation 4 Transactions of the American Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Calculus of Variations and Partial Differential Equations 4 Discrete and Continuous Dynamical Systems 4 Communications on Pure and Applied Analysis 4 Advances in Difference Equations 4 Journal of Theoretical Biology 4 Philosophical Transactions of the Royal Society of London. A. 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Second Series 2 Multiscale Modeling & Simulation 2 Analysis and Applications (Singapore) 2 Mathematical Biosciences and Engineering 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Communications in Computational Physics 2 Mathematical Modelling of Natural Phenomena 2 SN Partial Differential Equations and Applications 1 Acta Mechanica 1 Computer Physics Communications 1 International Journal of Control 1 Indian Journal of Pure & Applied Mathematics 1 Mathematical Biosciences 1 Physica A 1 Physics Reports 1 Reviews of Modern Physics 1 Theoretical and Mathematical Physics 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Theoretical and Computational Fluid Dynamics 1 Journal of Geometry and Physics 1 ACM Transactions on Mathematical Software 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of the Korean Mathematical Society 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Meccanica 1 Memoirs of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Quaestiones Mathematicae 1 SIAM Journal on Numerical Analysis 1 Tokyo Journal of Mathematics ...and 38 more Serials all top 5 Cited in 32 Fields 548 Partial differential equations (35-XX) 160 Biology and other natural sciences (92-XX) 138 Dynamical systems and ergodic theory (37-XX) 103 Ordinary differential equations (34-XX) 77 Numerical analysis (65-XX) 44 Fluid mechanics (76-XX) 17 Operator theory (47-XX) 15 Statistical mechanics, structure of matter (82-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 12 Optics, electromagnetic theory (78-XX) 12 Classical thermodynamics, heat transfer (80-XX) 9 Mechanics of deformable solids (74-XX) 8 Integral equations (45-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Probability theory and stochastic processes (60-XX) 7 Geophysics (86-XX) 7 Systems theory; control (93-XX) 6 Difference and functional equations (39-XX) 5 Real functions (26-XX) 4 Special functions (33-XX) 4 Mechanics of particles and systems (70-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Differential geometry (53-XX) 2 General and overarching topics; collections (00-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year