## Kolokolnikov, Theodore

Compute Distance To:
 Author ID: kolokolnikov.theodore Published as: Kolokolnikov, Theodore; Kolokolnikov, T.; Kolokolonikov, Theodore; Kolokolonikov, T. more...less
 Documents Indexed: 72 Publications since 2003 Co-Authors: 52 Co-Authors with 70 Joint Publications 1,247 Co-Co-Authors
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### Co-Authors

 2 single-authored 22 Ward, Michael J. 21 Wei, Juncheng 7 Iron, David 6 Xie, Shuangquan 5 Bertozzi, Andrea Louise 5 Kevrekidis, Panayotis G. 5 Tzou, Justin C. 3 Carretero-González, Ricardo 3 Evers, Joep H. M. 3 Gai, Chunyi 3 Rumsey, John R. 3 von Brecht, James H. 2 Alcolado, Adam 2 Chen, Chiun-Chuan 2 Erneux, Thomas 2 Fetecau, Razvan C. 2 Huang, Yanghong 2 Lindsay, Alan E. 2 McKay, Rebecca 2 Paquin-Lefebvre, Frédéric 2 Sun, Hui 2 Uminsky, David T. 1 Bielawski, Serge 1 Breslau, Jonah 1 Chaturapruek, Sorathan 1 Chavy-Waddy, Paul-Christopher 1 Cheb-Terrab, E. S. 1 Chen, Yuxin 1 Eswarathasan, Suresh 1 Huang, Chih-Chiang 1 Joly, Nicolas 1 Kang, Kyungkeun 1 Khalil, Nancy 1 Liu, Wangyi 1 Mackey, Alan 1 McCalla, Scott G. 1 Muir, Paul H. 1 Nishiura, Yasumasa 1 Nizette, Michel 1 Ou, Chunhua 1 Pavlovski, Mark 1 Peirce, Anthony P. 1 Ren, Xiaofeng 1 Smith-Roberge, Julien 1 Sun, Wentao 1 Taki, Majid 1 Ticknor, Chris 1 Titcombe, Michèle S. 1 Tlidi, Mustapha 1 Winter, Matthias 1 Yang, Wen 1 Yazdi, Daniel
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### Serials

 11 Physica D 8 Discrete and Continuous Dynamical Systems. Series B 8 SIAM Journal on Applied Dynamical Systems 7 European Journal of Applied Mathematics 5 Nonlinearity 5 SIAM Journal on Applied Mathematics 3 IMA Journal of Applied Mathematics 3 Journal of Differential Equations 3 Studies in Applied Mathematics 2 Journal of Mathematical Biology 2 Communications in Mathematical Sciences 1 Journal of Statistical Physics 1 The Mathematical Intelligencer 1 Applied Mathematics Letters 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Linear Algebra and its Applications 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Journal of Nonlinear Science 1 Chaos 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 Multiscale Modeling & Simulation 1 Inverse Problems in Science and Engineering 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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### Fields

 59 Partial differential equations (35-XX) 29 Biology and other natural sciences (92-XX) 10 Dynamical systems and ergodic theory (37-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Numerical analysis (65-XX) 4 Ordinary differential equations (34-XX) 3 Combinatorics (05-XX) 3 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 2 Mechanics of particles and systems (70-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

62 Publications have been cited 821 times in 479 Documents Cited by Year
Swarm dynamics and equilibria for a nonlocal aggregation model. Zbl 1288.92031
Fetecau, R. C.; Huang, Y.; Kolokolnikov, T.
2011
Predicting pattern formation in particle interactions. Zbl 1252.35056
von Brecht, James H.; Uminsky, David; Kolokolnikov, Theodore; Bertozzi, Andrea L.
2012
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
Ring patterns and their bifurcations in a nonlocal model of biological swarms. Zbl 1331.35044
Bertozzi, Andrea L.; Kolokolnikov, Theodore; Sun, Hui; Uminsky, David; von Brecht, James
2015
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Zbl 1090.35070
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J.
2005
Mesa-type patterns in the one-dimensional Brusselator and their stability. Zbl 1108.35088
Kolokolnikov, T.; Erneux, T.; Wei, J.
2006
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
Phytoplankton depth profiles and their transitions near the critical sinking velocity. Zbl 1204.92068
Kolokolnikov, Theodore; Ou, Chunhua; Yuan, Yuan
2009
Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. Zbl 1364.35151
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T.
2015
Crime modeling with Lévy flights. Zbl 1280.35158
Chaturapruek, Sorathan; Breslau, Jonah; Yazdi, Daniel; Kolokolnikov, Theodore; McCalla, Scott G.
2013
Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. Zbl 1063.35024
Kolokolnikov, Theodore; Ward, Michael J.
2003
The stability and dynamics of a spike in the 1D Keller-Segel model. Zbl 1133.35058
Kang, K.; Kolokolnikov, T.; Ward, M. J.
2007
Diffuse interface surface tension models in an expanding flow. Zbl 1272.35025
Bertozzi, Andrea; Kolokolnikov, Theodore; Liu, Wangyi
2012
Pattern formation in bacterial colonies with density-dependent diffusion. Zbl 1407.92030
Smith-Roberge, Julien; Iron, David; Kolokolnikov, Theodore
2019
Patterned vegetation, tipping points, and the rate of climate change. Zbl 1375.92078
Chen, Yuxin; Kolokolnikov, Theodore; Tzou, Justin; Gai, Chunyi
2015
Moving and jumping spot in a two-dimensional reaction-diffusion model. Zbl 1404.35232
Xie, Shuangquan; Kolokolnikov, Theodore
2017
Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. Zbl 1145.35388
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2006
Stability of spiky solutions in a competition model with cross-diffusion. Zbl 1259.35018
Kolokolnikov, Theodore; Wei, Juncheng
2011
The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. Zbl 1125.35048
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Two-species particle aggregation and stability of co-dimension one solutions. Zbl 1304.35081
Mackey, Alan; Kolokolnikov, Theodore; Bertozzi, Andrea L.
2014
Singular patterns for an aggregation model with a confining potential. Zbl 1286.35036
Kolokolnikov, Theodore; Huang, Yanghong; Pavlovski, Mark
2013
On ring-like solutions for the Gray-Scott model: existence, instability and self-replicating rings. Zbl 1085.35019
Kolokolnikov, T.; Wei, J.
2005
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. Zbl 1434.35019
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J.
2017
Metastable states for an aggregation model with noise. Zbl 1359.35201
Evers, Joep H. M.; Kolokolnikov, Theodore
2016
Pattern formation in a reaction-diffusion system with space-dependent feed rate. Zbl 1397.35023
Kolokolnikov, Theodore; Wei, Juncheng
2018
A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose-Einstein condensates. Zbl 1371.82060
Kolokolnikov, T.; Kevrekidis, P. G.; Carretero-González, R.
2014
Swarming on random graphs. Zbl 1269.82047
von Brecht, James; Kolokolnikov, Theodore; Bertozzi, Andrea L.; Sun, Hui
2013
Pulse-splitting for some reaction-diffusion systems in one-space dimension. Zbl 1145.35401
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. Zbl 1105.35132
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2006
Basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth. Zbl 1323.35085
2014
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Zbl 1063.35084
Kolokolnikov, Theodore; Ward, Michael J.
2004
Self-replication of mesa patterns in reaction-diffusion systems. Zbl 1136.35002
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007
Positive clustered layered solutions for the Gierer-Meinhardt system. Zbl 1155.35022
Kolokolonikov, T.; Wei, Juncheng
2008
Equilibria for an aggregation model with two species. Zbl 1387.35587
Evers, Joep H. M.; Fetecau, Razvan C.; Kolokolnikov, Theodore
2017
First-order ordinary differential equations, symmetries and linear transformations. Zbl 1047.34037
Cheb-Terrab, E. S.; Kolokolnikov, T.
2003
Introduction: Dissipative localized structures in extended systems. Zbl 1163.37376
Tlidi, Mustapha; Taki, Majid; Kolokolnikov, Theodore
2007
Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates. Zbl 1179.37120
Kolokolnikov, Theodore; Wei, Juncheng; Winter, Matthias
2009
On large ring solutions for Gierer-Meinhardt system in $$\mathbb R^3$$. Zbl 1286.35102
Kolokolnikov, Theodore; Wei, Juncheng; Yang, Wen
2013
Stability transitions and dynamics of mesa patterns near the shadow limit of reaction-diffusion systems in one space dimension. Zbl 1257.35037
McKay, Rebecca; Kolokolnikov, Theodore
2012
Smoke-ring solutions of Gierer-Meinhardt system in $$\mathbb{R}^{3}$$. Zbl 1219.35329
Kolokolnikov, Theodore; Ren, Xiaofeng
2011
Simple PDE model of spot replication in any dimension. Zbl 1263.35141
Chen, Chiun-Chuan; Kolokolnikov, Theodore
2012
Stable asymmetric spike equilibria for the Gierer-Meinhardt model with a precursor field. Zbl 1460.35014
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2020
Maximizing algebraic connectivity for certain families of graphs. Zbl 1307.05141
Kolokolnikov, T.
2015
Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation. Zbl 1364.35326
Carretero-González, R.; Kevrekidis, P. G.; Kolokolnikov, T.
2016
Stabilizing a homoclinic stripe. Zbl 1425.35100
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng
2018
Localized outbreaks in an S-I-R model with diffusion. Zbl 1439.35490
Gai, Chunyi; Iron, David; Kolokolnikov, Theodore
2020
Interface oscillations in reaction-diffusion systems above the Hopf bifurcation. Zbl 1258.35021
McKay, Rebecca; Kolokolnikov, Theodore; Muir, Paul
2012
Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap. Zbl 1402.82020
Xie, Shuangquan; Kevrekidis, Panayotis G.; Kolokolnikov, Theodore
2018
Competition instabilities of spike patterns for the 1D Gierer-Meinhardt and Schnakenberg models are subcritical. Zbl 1456.35013
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2021
The transition to a point constraint in a mixed biharmonic eigenvalue problem. Zbl 1319.35120
Lindsay, A. E.; Ward, M. J.; Kolokolnikov, T.
2015
Hexagonal spike clusters for some PDE’s in 2D. Zbl 1452.35015
Kolokolnikov, Theodore; Wei, Juncheng
2020
Spike density distribution for the Gierer-Meinhardt model with precursor. Zbl 1453.35026
Kolokolnikov, Theodore; Xie, Shuangquan
2020
Weakly nonlinear analysis of vortex formation in a dissipative variant of the Gross-Pitaevskii equation. Zbl 1342.35355
Tzou, J. C.; Kevrekidis, P. G.; Kolokolnikov, T.; Carretero-González, R.
2016
A local PDE model of aggregation formation in bacterial colonies. Zbl 1354.35167
2016
Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems. Zbl 1331.35189
Xie, Shuangquan; Kolokolnikov, Theodore
2016
Stability of curved interfaces in the perturbed two-dimensional Allen – Cahn system. Zbl 1184.35021
Iron, David; Kolokolonikov, Theodore; Rumsey, John; Wei, Juncheng
2009
The Q-switching instability in passively mode-locked lasers. Zbl 1136.78325
Kolokolnikov, Theodore; Nizette, Michel; Erneux, Thomas; Joly, Nicolas; Bielawski, Serge
2006
Critical exponent of a simple model of spot replication. Zbl 1397.35135
Chen, Chiun-Chuan; Huang, Chih-Chiang; Kolokolnikov, Theodore
2017
Competition instabilities of spike patterns for the 1D Gierer-Meinhardt and Schnakenberg models are subcritical. Zbl 1456.35013
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2021
Stable asymmetric spike equilibria for the Gierer-Meinhardt model with a precursor field. Zbl 1460.35014
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J.
2020
Localized outbreaks in an S-I-R model with diffusion. Zbl 1439.35490
Gai, Chunyi; Iron, David; Kolokolnikov, Theodore
2020
Hexagonal spike clusters for some PDE’s in 2D. Zbl 1452.35015
Kolokolnikov, Theodore; Wei, Juncheng
2020
Spike density distribution for the Gierer-Meinhardt model with precursor. Zbl 1453.35026
Kolokolnikov, Theodore; Xie, Shuangquan
2020
Pattern formation in bacterial colonies with density-dependent diffusion. Zbl 1407.92030
Smith-Roberge, Julien; Iron, David; Kolokolnikov, Theodore
2019
Pattern formation in a reaction-diffusion system with space-dependent feed rate. Zbl 1397.35023
Kolokolnikov, Theodore; Wei, Juncheng
2018
Stabilizing a homoclinic stripe. Zbl 1425.35100
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng
2018
Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap. Zbl 1402.82020
Xie, Shuangquan; Kevrekidis, Panayotis G.; Kolokolnikov, Theodore
2018
Moving and jumping spot in a two-dimensional reaction-diffusion model. Zbl 1404.35232
Xie, Shuangquan; Kolokolnikov, Theodore
2017
The stability and slow dynamics of localized spot patterns for the 3-D Schnakenberg reaction-diffusion model. Zbl 1434.35019
Tzou, J. C.; Xie, S.; Kolokolnikov, T.; Ward, M. J.
2017
Equilibria for an aggregation model with two species. Zbl 1387.35587
Evers, Joep H. M.; Fetecau, Razvan C.; Kolokolnikov, Theodore
2017
Critical exponent of a simple model of spot replication. Zbl 1397.35135
Chen, Chiun-Chuan; Huang, Chih-Chiang; Kolokolnikov, Theodore
2017
Metastable states for an aggregation model with noise. Zbl 1359.35201
Evers, Joep H. M.; Kolokolnikov, Theodore
2016
Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation. Zbl 1364.35326
Carretero-González, R.; Kevrekidis, P. G.; Kolokolnikov, T.
2016
Weakly nonlinear analysis of vortex formation in a dissipative variant of the Gross-Pitaevskii equation. Zbl 1342.35355
Tzou, J. C.; Kevrekidis, P. G.; Kolokolnikov, T.; Carretero-González, R.
2016
A local PDE model of aggregation formation in bacterial colonies. Zbl 1354.35167
2016
Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems. Zbl 1331.35189
Xie, Shuangquan; Kolokolnikov, Theodore
2016
Ring patterns and their bifurcations in a nonlocal model of biological swarms. Zbl 1331.35044
Bertozzi, Andrea L.; Kolokolnikov, Theodore; Sun, Hui; Uminsky, David; von Brecht, James
2015
Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. Zbl 1364.35151
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T.
2015
Patterned vegetation, tipping points, and the rate of climate change. Zbl 1375.92078
Chen, Yuxin; Kolokolnikov, Theodore; Tzou, Justin; Gai, Chunyi
2015
Maximizing algebraic connectivity for certain families of graphs. Zbl 1307.05141
Kolokolnikov, T.
2015
The transition to a point constraint in a mixed biharmonic eigenvalue problem. Zbl 1319.35120
Lindsay, A. E.; Ward, M. J.; Kolokolnikov, T.
2015
The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime. Zbl 1304.35051
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2014
Two-species particle aggregation and stability of co-dimension one solutions. Zbl 1304.35081
Mackey, Alan; Kolokolnikov, Theodore; Bertozzi, Andrea L.
2014
A tale of two distributions: from few to many vortices in quasi-two-dimensional Bose-Einstein condensates. Zbl 1371.82060
Kolokolnikov, T.; Kevrekidis, P. G.; Carretero-González, R.
2014
Basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth. Zbl 1323.35085
2014
Crime modeling with Lévy flights. Zbl 1280.35158
Chaturapruek, Sorathan; Breslau, Jonah; Yazdi, Daniel; Kolokolnikov, Theodore; McCalla, Scott G.
2013
Singular patterns for an aggregation model with a confining potential. Zbl 1286.35036
Kolokolnikov, Theodore; Huang, Yanghong; Pavlovski, Mark
2013
Swarming on random graphs. Zbl 1269.82047
von Brecht, James; Kolokolnikov, Theodore; Bertozzi, Andrea L.; Sun, Hui
2013
On large ring solutions for Gierer-Meinhardt system in $$\mathbb R^3$$. Zbl 1286.35102
Kolokolnikov, Theodore; Wei, Juncheng; Yang, Wen
2013
Predicting pattern formation in particle interactions. Zbl 1252.35056
von Brecht, James H.; Uminsky, David; Kolokolnikov, Theodore; Bertozzi, Andrea L.
2012
Diffuse interface surface tension models in an expanding flow. Zbl 1272.35025
Bertozzi, Andrea; Kolokolnikov, Theodore; Liu, Wangyi
2012
Stability transitions and dynamics of mesa patterns near the shadow limit of reaction-diffusion systems in one space dimension. Zbl 1257.35037
McKay, Rebecca; Kolokolnikov, Theodore
2012
Simple PDE model of spot replication in any dimension. Zbl 1263.35141
Chen, Chiun-Chuan; Kolokolnikov, Theodore
2012
Interface oscillations in reaction-diffusion systems above the Hopf bifurcation. Zbl 1258.35021
McKay, Rebecca; Kolokolnikov, Theodore; Muir, Paul
2012
Swarm dynamics and equilibria for a nonlocal aggregation model. Zbl 1288.92031
Fetecau, R. C.; Huang, Y.; Kolokolnikov, T.
2011
Stability of spiky solutions in a competition model with cross-diffusion. Zbl 1259.35018
Kolokolnikov, Theodore; Wei, Juncheng
2011
Smoke-ring solutions of Gierer-Meinhardt system in $$\mathbb{R}^{3}$$. Zbl 1219.35329
Kolokolnikov, Theodore; Ren, Xiaofeng
2011
An asymptotic analysis of the mean first passage time for narrow escape problems. I: Two-dimensional domains. Zbl 1203.35023
Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T.
2010
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. Zbl 1178.35039
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2009
Phytoplankton depth profiles and their transitions near the critical sinking velocity. Zbl 1204.92068
Kolokolnikov, Theodore; Ou, Chunhua; Yuan, Yuan
2009
Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates. Zbl 1179.37120
Kolokolnikov, Theodore; Wei, Juncheng; Winter, Matthias
2009
Stability of curved interfaces in the perturbed two-dimensional Allen – Cahn system. Zbl 1184.35021
Iron, David; Kolokolonikov, Theodore; Rumsey, John; Wei, Juncheng
2009
Positive clustered layered solutions for the Gierer-Meinhardt system. Zbl 1155.35022
Kolokolonikov, T.; Wei, Juncheng
2008
The stability and dynamics of a spike in the 1D Keller-Segel model. Zbl 1133.35058
Kang, K.; Kolokolnikov, T.; Ward, M. J.
2007
Self-replication of mesa patterns in reaction-diffusion systems. Zbl 1136.35002
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007
Introduction: Dissipative localized structures in extended systems. Zbl 1163.37376
Tlidi, Mustapha; Taki, Majid; Kolokolnikov, Theodore
2007
Mesa-type patterns in the one-dimensional Brusselator and their stability. Zbl 1108.35088
Kolokolnikov, T.; Erneux, T.; Wei, J.
2006
The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng
2006
Zigzag and breakup instabilities of stripes and rings in the two-dimensional Gray-Scott model. Zbl 1145.35388
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2006
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model. Zbl 1105.35132
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2006
The Q-switching instability in passively mode-locked lasers. Zbl 1136.78325
Kolokolnikov, Theodore; Nizette, Michel; Erneux, Thomas; Joly, Nicolas; Bielawski, Serge
2006
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Zbl 1136.35003
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: The low feed-rate regime. Zbl 1145.65328
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Zbl 1090.35070
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J.
2005
The existence and stability of spike equilibria in the one-dimensional Gray – Scott model on a finite domain. Zbl 1125.35048
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
On ring-like solutions for the Gray-Scott model: existence, instability and self-replicating rings. Zbl 1085.35019
Kolokolnikov, T.; Wei, J.
2005
Pulse-splitting for some reaction-diffusion systems in one-space dimension. Zbl 1145.35401
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng
2005
Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Zbl 1063.35084
Kolokolnikov, Theodore; Ward, Michael J.
2004
Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. Zbl 1063.35024
Kolokolnikov, Theodore; Ward, Michael J.
2003
First-order ordinary differential equations, symmetries and linear transformations. Zbl 1047.34037
Cheb-Terrab, E. S.; Kolokolnikov, T.
2003
all top 5

### Cited by 718 Authors

 49 Ward, Michael J. 35 Carrillo de la Plata, José Antonio 34 Kolokolnikov, Theodore 28 Wei, Juncheng 14 Bertozzi, Andrea Louise 14 Tzou, Justin C. 12 Fetecau, Razvan C. 10 Doelman, Arjen 8 Chen, Xinfu 8 Holcman, David 8 Shi, Junping 8 Wang, Zhian 7 Huang, Yanghong 7 Iron, David 7 Lou, Yuan 7 von Brecht, James H. 7 Xie, Shuangquan 6 Craig, Katy 6 Kevrekidis, Panayotis G. 6 Lam, King-Yeung 6 Lawley, Sean D. 6 Lindsay, Alan E. 6 Topaloglu, Ihsan 6 Wang, Qi 6 Winter, Matthias 6 Yao, Yao 6 You, Yuncheng 5 Gai, Chunyi 5 Iyaniwura, Sarafa A. 5 Ma, Manjun 5 Nec, Yana 5 Nishiura, Yasumasa 5 Patacchini, Francesco Saverio 5 Peng, Rui 5 van Heijster, Peter 5 Zhang, Yajing 5 Zhou, Jun 4 Breña-Medina, Víctor F. 4 Hao, Jianghao 4 Hillen, Thomas 4 Kuto, Kousuke 4 Lai, Xin 4 Laurent, Thomas 4 Lim, Tongseok 4 Qin, Cong 4 Rademacher, Jens Diederich Michael 4 Rumsey, John R. 4 Scardia, Lucia 4 Schuss, Zeev 4 Short, Martin B. 4 Sun, Weiran 4 Tlidi, Mustapha 4 Tse, Wang Hung 4 Wang, Chuntian 4 Wang, Li 4 Wei, Junjie 3 Aguareles, Maria 3 Avitabile, Daniele 3 Balagué, Daniel 3 Bastiaansen, Robbin 3 Bellomo, Nicola 3 Bernoff, Andrew J. 3 Champneys, Alan R. 3 Chirilus-Bruckner, Martina 3 Colombi, Annachiara 3 Degond, Pierre 3 Düring, Bertram 3 Evers, Joep H. M. 3 Gomez, Daniel 3 Grebenkov, Denis S. 3 Ha, Seung-Yeal 3 Kreusser, Lisa Maria 3 Lombardo, Maria Carmela 3 Luo, Ting 3 Martin, Stephan 3 Mateu, Joan 3 McCann, Robert J. 3 Messenger, Daniel A. 3 Mora, Maria Giovanna 3 Motsch, Sébastien 3 Moyles, Iain R. 3 Rondi, Luca 3 Rottschäfer, Vivi 3 Sammartino, Marco Maria Luigi 3 Schmidtchen, Markus 3 Schönlieb, Carola-Bibiane 3 Scianna, Marco 3 Shu, Ruiwen 3 Slepčev, Dejan 3 Tadmor, Eitan 3 Tzou, Leo 3 Uminsky, David T. 3 Verdera, Joan 3 Winkler, Michael 3 Wu, Jianhua 3 Zhang, Guohong 2 Al Saadi, Fahad 2 Bénichou, Olivier 2 Bilyk, Dmitry 2 Caginalp, Carey ...and 618 more Authors
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### Cited in 120 Serials

 32 SIAM Journal on Applied Dynamical Systems 27 Physica D 20 Journal of Differential Equations 20 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 19 European Journal of Applied Mathematics 18 Journal of Mathematical Biology 17 Discrete and Continuous Dynamical Systems. Series B 15 SIAM Journal on Applied Mathematics 14 Journal of Statistical Physics 13 Journal of Nonlinear Science 11 Discrete and Continuous Dynamical Systems 10 Chaos 9 Journal of Mathematical Analysis and Applications 9 Nonlinearity 9 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Bulletin of Mathematical Biology 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 SIAM Journal on Mathematical Analysis 8 Communications in Nonlinear Science and Numerical Simulation 7 Archive for Rational Mechanics and Analysis 7 Journal of Dynamics and Differential Equations 7 Nonlinear Analysis. Real World Applications 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Multiscale Modeling & Simulation 5 Applied Mathematics and Computation 5 Studies in Applied Mathematics 5 Calculus of Variations and Partial Differential Equations 5 Communications on Pure and Applied Analysis 5 Journal of Biological Dynamics 4 Communications in Mathematical Physics 4 Applied Mathematics Letters 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Mathematical Biosciences and Engineering 4 Journal of Theoretical Biology 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Computers & Mathematics with Applications 3 Journal of Computational Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Mathematics of Computation 3 Chaos, Solitons and Fractals 3 Mathematics and Computers in Simulation 3 Acta Applicandae Mathematicae 3 Networks and Heterogeneous Media 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Mathematics in Applied Sciences and Engineering 2 Applicable Analysis 2 International Journal of Control 2 Physica A 2 Indiana University Mathematics Journal 2 Journal of Scientific Computing 2 SIAM Review 2 Journal of Mathematical Sciences (New York) 2 NoDEA. Nonlinear Differential Equations and Applications 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Analysis and Applications (Singapore) 2 Communications in Computational Physics 1 Computers and Fluids 1 Computer Physics Communications 1 Discrete Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Engineering Mathematics 1 Journal of Mathematical Physics 1 Physics Letters. A 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Journal of the Korean Mathematical Society 1 Journal of the Mathematical Society of Japan 1 Mathematische Annalen 1 Mathematics of Operations Research 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Operations Research 1 Ricerche di Matematica 1 SIAM Journal on Control and Optimization 1 Advances in Applied Mathematics 1 Chinese Annals of Mathematics. Series B 1 Applied Numerical Mathematics 1 Revista Matemática Iberoamericana 1 Computational Mechanics 1 Mathematical and Computer Modelling 1 Science in China. Series A 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Stochastic Processes and their Applications 1 SIAM Journal on Scientific Computing 1 Journal of the Egyptian Mathematical Society 1 Advances in Computational Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 Nonlinear Dynamics 1 Abstract and Applied Analysis 1 Taiwanese Journal of Mathematics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society 1 Journal of Mathematical Fluid Mechanics 1 Acta Mathematica Sinica. English Series 1 Communications in Contemporary Mathematics 1 The ANZIAM Journal ...and 20 more Serials
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### Cited in 38 Fields

 355 Partial differential equations (35-XX) 207 Biology and other natural sciences (92-XX) 54 Dynamical systems and ergodic theory (37-XX) 50 Statistical mechanics, structure of matter (82-XX) 46 Numerical analysis (65-XX) 44 Ordinary differential equations (34-XX) 38 Probability theory and stochastic processes (60-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 30 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 24 Fluid mechanics (76-XX) 17 Integral equations (45-XX) 17 Mechanics of particles and systems (70-XX) 9 Global analysis, analysis on manifolds (58-XX) 9 Mechanics of deformable solids (74-XX) 9 Systems theory; control (93-XX) 8 Combinatorics (05-XX) 7 Operator theory (47-XX) 6 Operations research, mathematical programming (90-XX) 6 Information and communication theory, circuits (94-XX) 5 Potential theory (31-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Differential geometry (53-XX) 4 Computer science (68-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 3 Quantum theory (81-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Convex and discrete geometry (52-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Geophysics (86-XX)