Gai, Chunyi; Kolokolnikov, Theodore Resource-mediated competition between two plant species with different rates of water intake. (English) Zbl 1514.35038 SIAM J. Appl. Math. 83, No. 2, 576-602 (2023). MSC: 35B36 35B25 35B35 35B40 35K51 35K57 35Q92 PDFBibTeX XMLCite \textit{C. Gai} and \textit{T. Kolokolnikov}, SIAM J. Appl. Math. 83, No. 2, 576--602 (2023; Zbl 1514.35038) Full Text: DOI
Al Saadi, Fahad; Champneys, Alan; Gai, Chunyi; Kolokolnikov, Theodore Spikes and localised patterns for a novel Schnakenberg model in the semi-strong interaction regime. (English) Zbl 1504.35029 Eur. J. Appl. Math. 33, No. 1, 133-152 (2022). MSC: 35B25 35B32 35B36 35K51 35K57 92C15 34E13 PDFBibTeX XMLCite \textit{F. Al Saadi} et al., Eur. J. Appl. Math. 33, No. 1, 133--152 (2022; Zbl 1504.35029) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael A ring of spikes in a Schnakenberg model. (English) Zbl 1498.35026 Physica D 441, Article ID 133521, 13 p. (2022). MSC: 35B25 35K51 35K57 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{M. Ward}, Physica D 441, Article ID 133521, 13 p. (2022; Zbl 1498.35026) Full Text: DOI
Xie, Shuangquan; Kolokolnikov, Theodore; Nishiura, Yasumasa Complex oscillatory motion of multiple spikes in a three-component Schnakenberg system. (English) Zbl 1469.35019 Nonlinearity 34, No. 8, 5708-5743 (2021). MSC: 35B25 35B32 35K51 35K57 35B40 PDFBibTeX XMLCite \textit{S. Xie} et al., Nonlinearity 34, No. 8, 5708--5743 (2021; Zbl 1469.35019) Full Text: DOI arXiv
Kolokolnikov, Theodore; Paquin-Lefebvre, Frédéric; Ward, Michael J. Competition instabilities of spike patterns for the 1D Gierer-Meinhardt and Schnakenberg models are subcritical. (English) Zbl 1456.35013 Nonlinearity 34, No. 1, 273-312 (2021). MSC: 35B25 35B32 35B35 35B36 35K57 92C15 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Nonlinearity 34, No. 1, 273--312 (2021; Zbl 1456.35013) Full Text: DOI
Buttenschoen, Andreas; Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng Cops-on-the-dots: the linear stability of crime hotspots for a 1-D reaction-diffusion model of urban crime. (English) Zbl 1504.35031 Eur. J. Appl. Math. 31, No. 5, 871-917 (2020). MSC: 35B25 35B32 35B35 35K51 35K57 PDFBibTeX XMLCite \textit{A. Buttenschoen} et al., Eur. J. Appl. Math. 31, No. 5, 871--917 (2020; Zbl 1504.35031) Full Text: DOI
Kolokolnikov, Theodore; Wei, Juncheng Hexagonal spike clusters for some PDE’s in 2D. (English) Zbl 1452.35015 Discrete Contin. Dyn. Syst., Ser. B 25, No. 10, 4057-4070 (2020). MSC: 35B25 35K57 35B36 35J61 35J47 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{J. Wei}, Discrete Contin. Dyn. Syst., Ser. B 25, No. 10, 4057--4070 (2020; Zbl 1452.35015) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael; Tzou, Justin; Wei, Juncheng Stabilizing a homoclinic stripe. (English) Zbl 1425.35100 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2135, Article ID 20180110, 13 p. (2018). MSC: 35K57 35K51 35M33 35B25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2135, Article ID 20180110, 13 p. (2018; Zbl 1425.35100) Full Text: DOI Link
Xie, Shuangquan; Kolokolnikov, Theodore Moving and jumping spot in a two-dimensional reaction-diffusion model. (English) Zbl 1404.35232 Nonlinearity 30, No. 4, 1536-1563 (2017). MSC: 35K51 35B40 35C20 35K57 35B25 35B32 35B36 92C15 PDFBibTeX XMLCite \textit{S. Xie} and \textit{T. Kolokolnikov}, Nonlinearity 30, No. 4, 1536--1563 (2017; Zbl 1404.35232) Full Text: DOI
Xie, Shuangquan; Kolokolnikov, Theodore Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems. (English) Zbl 1331.35189 Discrete Contin. Dyn. Syst., Ser. B 21, No. 3, 959-975 (2016). MSC: 35K57 35B36 35B25 PDFBibTeX XMLCite \textit{S. Xie} and \textit{T. Kolokolnikov}, Discrete Contin. Dyn. Syst., Ser. B 21, No. 3, 959--975 (2016; Zbl 1331.35189) Full Text: DOI
Tzou, J. C.; Ward, M. J.; Kolokolnikov, T. Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems. (English) Zbl 1364.35151 Physica D 290, 24-43 (2015). MSC: 35K57 35B32 37G10 37M05 PDFBibTeX XMLCite \textit{J. C. Tzou} et al., Physica D 290, 24--43 (2015; Zbl 1364.35151) Full Text: DOI arXiv
Chen, Chiun-Chuan; Kolokolnikov, Theodore Simple PDE model of spot replication in any dimension. (English) Zbl 1263.35141 SIAM J. Math. Anal. 44, No. 5, 3564-3593 (2012). Reviewer: Jiaqi Mo (Wuhu) MSC: 35K57 35Q92 35B25 35B32 PDFBibTeX XMLCite \textit{C.-C. Chen} and \textit{T. Kolokolnikov}, SIAM J. Math. Anal. 44, No. 5, 3564--3593 (2012; Zbl 1263.35141) Full Text: DOI
McKay, Rebecca; Kolokolnikov, Theodore; Muir, Paul Interface oscillations in reaction-diffusion systems above the Hopf bifurcation. (English) Zbl 1258.35021 Discrete Contin. Dyn. Syst., Ser. B 17, No. 7, 2523-2543 (2012). Reviewer: Qin Mengzhao (Beijing) MSC: 35B32 35K57 37M05 37M20 35K51 35K58 35B25 PDFBibTeX XMLCite \textit{R. McKay} et al., Discrete Contin. Dyn. Syst., Ser. B 17, No. 7, 2523--2543 (2012; Zbl 1258.35021) Full Text: DOI
McKay, Rebecca; Kolokolnikov, Theodore Stability transitions and dynamics of mesa patterns near the shadow limit of reaction-diffusion systems in one space dimension. (English) Zbl 1257.35037 Discrete Contin. Dyn. Syst., Ser. B 17, No. 1, 191-220 (2012). Reviewer: Michael I. Gil’ (Beer-Sheva) MSC: 35B35 35K57 35K51 35B36 35B25 PDFBibTeX XMLCite \textit{R. McKay} and \textit{T. Kolokolnikov}, Discrete Contin. Dyn. Syst., Ser. B 17, No. 1, 191--220 (2012; Zbl 1257.35037) Full Text: DOI
Kolokolnikov, Theodore; Wei, Juncheng Stability of spiky solutions in a competition model with cross-diffusion. (English) Zbl 1259.35018 SIAM J. Appl. Math. 71, No. 4, 1428-1457 (2011). Reviewer: Oleh Omel’chenko (Berlin) MSC: 35B25 35K57 35B36 35K58 35K51 35B35 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{J. Wei}, SIAM J. Appl. Math. 71, No. 4, 1428--1457 (2011; Zbl 1259.35018) Full Text: DOI Link
Iron, David; Kolokolonikov, Theodore; Rumsey, John; Wei, Juncheng Stability of curved interfaces in the perturbed two-dimensional Allen – Cahn system. (English) Zbl 1184.35021 SIAM J. Appl. Math. 69, No. 5, 1228-1243 (2009). Reviewer: Galina Bizhanova (Almaty) MSC: 35B25 35B40 35K57 35B35 35K58 35K20 PDFBibTeX XMLCite \textit{D. Iron} et al., SIAM J. Appl. Math. 69, No. 5, 1228--1243 (2009; Zbl 1184.35021) Full Text: DOI
Kolokolnikov, Theodore; Wei, Juncheng; Winter, Matthias Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates. (English) Zbl 1179.37120 Physica D 238, No. 16, 1695-1710 (2009). Reviewer: Guy Katriel (Haifa) MSC: 37N25 92B15 35K57 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Physica D 238, No. 16, 1695--1710 (2009; Zbl 1179.37120) Full Text: DOI
Kolokolnikov, T.; Ward, M. J.; Wei, J. Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain. (English) Zbl 1178.35039 J. Nonlinear Sci. 19, No. 1, 1-56 (2009). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 92E20 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., J. Nonlinear Sci. 19, No. 1, 1--56 (2009; Zbl 1178.35039) Full Text: DOI Link
Kolokolnikov, T.; Ward, M. J.; Wei, J. Self-replication of mesa patterns in reaction-diffusion systems. (English) Zbl 1136.35002 Physica D 236, No. 2, 104-122 (2007). MSC: 35B25 35K57 35K50 35B32 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Physica D 236, No. 2, 104--122 (2007; Zbl 1136.35002) Full Text: DOI arXiv
Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. (English) Zbl 1210.35016 SIAM J. Appl. Dyn. Syst. 5, No. 2, 313-363 (2006). MSC: 35B25 35K57 35P30 37N25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., SIAM J. Appl. Dyn. Syst. 5, No. 2, 313--363 (2006; Zbl 1210.35016) Full Text: DOI Link
Kolokolnikov, Theodore; Ward, Michael J.; Wei, Juncheng Pulse-splitting for some reaction-diffusion systems in one-space dimension. (English) Zbl 1145.35401 Stud. Appl. Math. 114, No. 2, 115-165 (2005). MSC: 35K57 35B25 35K50 92D25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Stud. Appl. Math. 114, No. 2, 115--165 (2005; Zbl 1145.35401) Full Text: DOI
Kolokolnikov, T.; Wei, J. On ring-like solutions for the Gray-Scott model: existence, instability and self-replicating rings. (English) Zbl 1085.35019 Eur. J. Appl. Math. 16, No. 2, 201-237 (2005). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 35B35 35K45 35K50 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{J. Wei}, Eur. J. Appl. Math. 16, No. 2, 201--237 (2005; Zbl 1085.35019) Full Text: DOI
Kolokolnikov, T.; Titcombe, M. S.; Ward, M. J. Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. (English) Zbl 1090.35070 Eur. J. Appl. Math. 16, No. 2, 161-200 (2005). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 35J25 35P05 35B25 35C20 49J20 65N25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Eur. J. Appl. Math. 16, No. 2, 161--200 (2005; Zbl 1090.35070) Full Text: DOI
Kolokolnikov, Theodore; Ward, Michael J. Reduced wave Green’s functions and their effect on the dynamics of a spike for the Gierer-Meinhardt model. (English) Zbl 1063.35024 Eur. J. Appl. Math. 14, No. 5, 513-545 (2003). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B25 35K57 35K50 92C20 65M60 35B40 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{M. J. Ward}, Eur. J. Appl. Math. 14, No. 5, 513--545 (2003; Zbl 1063.35024) Full Text: DOI