Lv, Yehu Turing-Turing bifurcation in an activator-inhibitor system with gene expression time delay. (English) Zbl 07810034 Commun. Nonlinear Sci. Numer. Simul. 131, Article ID 107836, 32 p. (2024). MSC: 35B32 35B10 35K51 35K57 37G05 37L10 92D25 PDFBibTeX XMLCite \textit{Y. Lv}, Commun. Nonlinear Sci. Numer. Simul. 131, Article ID 107836, 32 p. (2024; Zbl 07810034) Full Text: DOI
Hill, Dan J.; Bramburger, Jason J.; Lloyd, David J. B. Dihedral rings of patterns emerging from a Turing bifurcation. (English) Zbl 07807845 Nonlinearity 37, No. 3, Article ID 035015, 39 p. (2024). MSC: 35B32 35B36 35J47 35J61 35K57 37L65 34C37 PDFBibTeX XMLCite \textit{D. J. Hill} et al., Nonlinearity 37, No. 3, Article ID 035015, 39 p. (2024; Zbl 07807845) Full Text: DOI arXiv OA License
Li, Junyan; Wu, Ruili Dynamic transition analysis for activator-substrate system. (English) Zbl 1523.37094 J. Nonlinear Math. Phys. 30, No. 3, 956-979 (2023). MSC: 37N25 92C15 35K57 PDFBibTeX XMLCite \textit{J. Li} and \textit{R. Wu}, J. Nonlinear Math. Phys. 30, No. 3, 956--979 (2023; Zbl 1523.37094) Full Text: DOI OA License
Nishiura, Yasumasa; Teramoto, Takashi; Ueda, Kei-Ichi Arbitrarily weak head-on collision can induce annihilation: the role of hidden instabilities. (English) Zbl 1525.35021 Japan J. Ind. Appl. Math. 40, No. 3, 1695-1743 (2023). MSC: 35B32 35B36 35K40 35K57 37L10 92E20 PDFBibTeX XMLCite \textit{Y. Nishiura} et al., Japan J. Ind. Appl. Math. 40, No. 3, 1695--1743 (2023; Zbl 1525.35021) Full Text: DOI arXiv OA License
Villar-Sepúlveda, Edgardo; Aguirre, Pablo; Breña-Medina, Víctor F. A case study of multiple wave solutions in a reaction-diffusion system using invariant manifolds and global bifurcations. (English) Zbl 1523.37098 SIAM J. Appl. Dyn. Syst. 22, No. 2, 918-950 (2023). MSC: 37N25 35K57 35B32 35Q92 35C07 92D25 PDFBibTeX XMLCite \textit{E. Villar-Sepúlveda} et al., SIAM J. Appl. Dyn. Syst. 22, No. 2, 918--950 (2023; Zbl 1523.37098) Full Text: DOI arXiv
Jiang, Zhibei; Yuan, Zhaohui; Huang, Lihong Dynamics analysis on a chronic epidemic model with diffusion. (English) Zbl 1512.35376 Discrete Contin. Dyn. Syst., Ser. B 28, No. 5, 3107-3135 (2023). MSC: 35K57 35B41 35K51 37N25 92D30 PDFBibTeX XMLCite \textit{Z. Jiang} et al., Discrete Contin. Dyn. Syst., Ser. B 28, No. 5, 3107--3135 (2023; Zbl 1512.35376) Full Text: DOI
Ding, Yuting; Liu, Gaoyang; Zheng, Liyuan Equivalence of MTS and CMR methods associated with the normal form of Hopf bifurcation for delayed reaction-diffusion equations. (English) Zbl 1507.35024 Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106976, 17 p. (2023). MSC: 35B32 35K51 35K57 37L10 PDFBibTeX XMLCite \textit{Y. Ding} et al., Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106976, 17 p. (2023; Zbl 1507.35024) Full Text: DOI
Khalil, Nancy; Iron, David; Kolokolnikov, Theodore Stability and dynamics of spike-type solutions to delayed Gierer-Meinhardt equations. (English) Zbl 1501.35412 Discrete Contin. Dyn. Syst., Ser. B 28, No. 2, 1185-1214 (2023). MSC: 35Q92 92E20 92C37 35K57 35B32 35B40 35B20 35B35 35C20 35E05 37L10 34E10 35R07 PDFBibTeX XMLCite \textit{N. Khalil} et al., Discrete Contin. Dyn. Syst., Ser. B 28, No. 2, 1185--1214 (2023; Zbl 1501.35412) Full Text: DOI
Dey, Subrata; Banerjee, Malay; Ghorai, Saktipada Analytical detection of stationary Turing pattern in a predator-prey system with generalist predator. (English) Zbl 1518.35592 Math. Model. Nat. Phenom. 17, Paper No. 33, 31 p. (2022). MSC: 35Q92 92D25 35B32 35B36 34C23 37G15 35A01 35A02 35B09 92-08 PDFBibTeX XMLCite \textit{S. Dey} et al., Math. Model. Nat. Phenom. 17, Paper No. 33, 31 p. (2022; Zbl 1518.35592) Full Text: DOI
Nishiura, Yasumasa; Watanabe, Takeshi Traveling pulses with oscillatory tails, figure-eight-like stack of isolas, and dynamics in heterogeneous media. (English) Zbl 1500.35086 Physica D 440, Article ID 133448, 35 p. (2022). MSC: 35C07 35K40 35K57 37L10 PDFBibTeX XMLCite \textit{Y. Nishiura} and \textit{T. Watanabe}, Physica D 440, Article ID 133448, 35 p. (2022; Zbl 1500.35086) Full Text: DOI arXiv
Asheghi, Rasoul Hopf bifurcation analysis in a Gierer-Meinhardt activator-inhibitor model. (English) Zbl 1495.35021 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 9, Article ID 2250132, 21 p. (2022). MSC: 35B32 35B35 35K51 35K57 37L10 92D25 PDFBibTeX XMLCite \textit{R. Asheghi}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 9, Article ID 2250132, 21 p. (2022; Zbl 1495.35021) Full Text: DOI
Doelman, Arjen Slow localized patterns in singularly perturbed two-component reaction-diffusion equations. (English) Zbl 1492.35019 Nonlinearity 35, No. 7, 3487-3559 (2022). MSC: 35B25 35B35 35B36 35C07 35K57 37C29 34D15 92D40 PDFBibTeX XMLCite \textit{A. Doelman}, Nonlinearity 35, No. 7, 3487--3559 (2022; Zbl 1492.35019) Full Text: DOI arXiv
Yang, Rui; Yu, Xiao-Qing Turing-Hopf bifurcation in diffusive Gierer-Meinhardt model. (English) Zbl 1487.35047 Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 4, Article ID 2250046, 20 p. (2022). MSC: 35B32 35B36 35K51 35K57 37L10 92C15 PDFBibTeX XMLCite \textit{R. Yang} and \textit{X.-Q. Yu}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 32, No. 4, Article ID 2250046, 20 p. (2022; Zbl 1487.35047) Full Text: DOI
Larios, Adam; Victor, Collin Continuous data assimilation with a moving cluster of data points for a reaction diffusion equation: a computational study. (English) Zbl 1528.65094 Commun. Comput. Phys. 29, No. 4, 1273-1298 (2021). MSC: 65N06 65M06 65F05 35K57 35K40 35K61 37C50 93B52 35Q93 34D06 35R60 PDFBibTeX XMLCite \textit{A. Larios} and \textit{C. Victor}, Commun. Comput. Phys. 29, No. 4, 1273--1298 (2021; Zbl 1528.65094) Full Text: DOI arXiv
Carter, Paul; Rademacher, Jens D. M.; Sandstede, Björn Pulse replication and accumulation of eigenvalues. (English) Zbl 1490.35034 SIAM J. Math. Anal. 53, No. 3, 3520-3576 (2021). Reviewer: Anna Ghazaryan (Oxford) MSC: 35B35 35P15 35C07 35B25 37L15 34E17 35K58 PDFBibTeX XMLCite \textit{P. Carter} et al., SIAM J. Math. Anal. 53, No. 3, 3520--3576 (2021; Zbl 1490.35034) Full Text: DOI arXiv
Chen, Shanshan; Shi, Junping; Zhang, Guohong Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. (English) Zbl 1466.35024 Discrete Contin. Dyn. Syst., Ser. B 26, No. 4, 1843-1866 (2021). MSC: 35B36 35B32 35B35 35K51 35K57 37L15 92C15 PDFBibTeX XMLCite \textit{S. Chen} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 4, 1843--1866 (2021; Zbl 1466.35024) Full Text: DOI
Bramburger, Jason J. Isolas of multi-pulse solutions to lattice dynamical systems. (English) Zbl 1466.39012 Proc. R. Soc. Edinb., Sect. A, Math. 151, No. 3, 916-952 (2021). MSC: 39A28 37L60 PDFBibTeX XMLCite \textit{J. J. Bramburger}, Proc. R. Soc. Edinb., Sect. A, Math. 151, No. 3, 916--952 (2021; Zbl 1466.39012) Full Text: DOI arXiv
Wong, Tony; Ward, Michael J. Weakly nonlinear analysis of peanut-shaped deformations for localized spots of singularly perturbed reaction-diffusion systems. (English) Zbl 1472.35026 SIAM J. Appl. Dyn. Syst. 19, No. 3, 2030-2058 (2020). MSC: 35B25 35B32 35B36 35B60 35K51 35K57 37G05 65P30 PDFBibTeX XMLCite \textit{T. Wong} and \textit{M. J. Ward}, SIAM J. Appl. Dyn. Syst. 19, No. 3, 2030--2058 (2020; Zbl 1472.35026) Full Text: DOI arXiv
García-Azpeitia, Carlos; Lessard, Jean-Philippe Free vibrations in a wave equation modeling MEMS. (English) Zbl 1477.35014 SIAM J. Appl. Dyn. Syst. 19, No. 4, 2749-2782 (2020). Reviewer: Alois Steindl (Wien) MSC: 35B10 35B32 37M20 37N15 74H45 35L72 35L20 PDFBibTeX XMLCite \textit{C. García-Azpeitia} and \textit{J.-P. Lessard}, SIAM J. Appl. Dyn. Syst. 19, No. 4, 2749--2782 (2020; Zbl 1477.35014) Full Text: DOI arXiv
Liu, Xijuan; Liu, Yun Codimension-two bifurcation analysis on a discrete Gierer-Meinhardt system. (English) Zbl 1460.39006 Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 16, Article ID 2050251, 14 p. (2020). MSC: 39A28 39A30 37G05 37G10 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Y. Liu}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 30, No. 16, Article ID 2050251, 14 p. (2020; Zbl 1460.39006) Full Text: DOI
Kolokolnikov, Theodore; Xie, Shuangquan Spike density distribution for the Gierer-Meinhardt model with precursor. (English) Zbl 1453.35026 Physica D 402, Article ID 132247, 7 p. (2020). MSC: 35B36 37M05 PDFBibTeX XMLCite \textit{T. Kolokolnikov} and \textit{S. Xie}, Physica D 402, Article ID 132247, 7 p. (2020; Zbl 1453.35026) Full Text: DOI
Avitabile, Daniele; Desroches, Mathieu; Veltz, Romain; Wechselberger, Martin Local theory for spatio-temporal canards and delayed bifurcations. (English) Zbl 1453.35020 SIAM J. Math. Anal. 52, No. 6, 5703-5747 (2020). MSC: 35B32 35K57 35R10 37L10 PDFBibTeX XMLCite \textit{D. Avitabile} et al., SIAM J. Math. Anal. 52, No. 6, 5703--5747 (2020; Zbl 1453.35020) Full Text: DOI arXiv
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J. Weakly nonlinear theory for oscillatory dynamics in a one-dimensional PDE-ODE model of membrane dynamics coupled by a bulk diffusion field. (English) Zbl 1446.37071 SIAM J. Appl. Math. 80, No. 3, 1520-1545 (2020). MSC: 37M20 65P30 35B36 35B35 34C15 74K15 70K55 70K50 PDFBibTeX XMLCite \textit{F. Paquin-Lefebvre} et al., SIAM J. Appl. Math. 80, No. 3, 1520--1545 (2020; Zbl 1446.37071) Full Text: DOI arXiv
Bramburger, Jason J.; Sandstede, Björn Localized patterns in planar bistable weakly coupled lattice systems. (English) Zbl 1447.37065 Nonlinearity 33, No. 7, 3500-3525 (2020). MSC: 37L60 37L10 35B36 PDFBibTeX XMLCite \textit{J. J. Bramburger} and \textit{B. Sandstede}, Nonlinearity 33, No. 7, 3500--3525 (2020; Zbl 1447.37065) Full Text: DOI
Bramburger, Jason J.; Sandstede, Björn Spatially localized structures in lattice dynamical systems. (English) Zbl 1440.37072 J. Nonlinear Sci. 30, No. 2, 603-644 (2020). MSC: 37K60 37K45 35Q56 35B36 PDFBibTeX XMLCite \textit{J. J. Bramburger} and \textit{B. Sandstede}, J. Nonlinear Sci. 30, No. 2, 603--644 (2020; Zbl 1440.37072) Full Text: DOI
Bastiaansen, Robbin; Chirilus-Bruckner, Martina; Doelman, Arjen Pulse solutions for an extended Klausmeier model with spatially varying coefficients. (English) Zbl 1431.35071 SIAM J. Appl. Dyn. Syst. 19, No. 1, 1-57 (2020). MSC: 35K57 35Q92 35B25 35B35 35C20 37B55 92D40 PDFBibTeX XMLCite \textit{R. Bastiaansen} et al., SIAM J. Appl. Dyn. Syst. 19, No. 1, 1--57 (2020; Zbl 1431.35071) Full Text: DOI arXiv
Wang, Jinliang; Li, You; Zhong, Shihong; Hou, Xiaojie Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system. (English) Zbl 1442.35214 Chaos Solitons Fractals 118, 1-17 (2019). MSC: 35K57 37M20 35B36 35B32 37G15 PDFBibTeX XMLCite \textit{J. Wang} et al., Chaos Solitons Fractals 118, 1--17 (2019; Zbl 1442.35214) Full Text: DOI
Chirilus-Bruckner, M.; van Heijster, P.; Ikeda, H.; Rademacher, J. D. M. Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system. (English) Zbl 1427.35118 J. Nonlinear Sci. 29, No. 6, 2911-2953 (2019). MSC: 35K57 35C07 37L10 35B25 35B35 PDFBibTeX XMLCite \textit{M. Chirilus-Bruckner} et al., J. Nonlinear Sci. 29, No. 6, 2911--2953 (2019; Zbl 1427.35118) Full Text: DOI arXiv
Jiang, Weihua; Wang, Hongbin; Cao, Xun Turing instability and Turing-Hopf bifurcation in diffusive Schnakenberg systems with gene expression time delay. (English) Zbl 1428.35033 J. Dyn. Differ. Equations 31, No. 4, 2223-2247 (2019). MSC: 35B32 35K51 35K58 35B36 37L10 PDFBibTeX XMLCite \textit{W. Jiang} et al., J. Dyn. Differ. Equations 31, No. 4, 2223--2247 (2019; Zbl 1428.35033) Full Text: DOI arXiv
Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J. Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. (English) Zbl 1428.37071 SIAM J. Appl. Dyn. Syst. 18, No. 3, 1334-1390 (2019). MSC: 37L10 35K57 37M20 35B35 35B36 65P30 PDFBibTeX XMLCite \textit{F. Paquin-Lefebvre} et al., SIAM J. Appl. Dyn. Syst. 18, No. 3, 1334--1390 (2019; Zbl 1428.37071) Full Text: DOI arXiv
Smith-Roberge, Julien; Iron, David; Kolokolnikov, Theodore Pattern formation in bacterial colonies with density-dependent diffusion. (English) Zbl 1407.92030 Eur. J. Appl. Math. 30, No. 1, 196-218 (2019). MSC: 92C17 92D25 35Q92 37D45 PDFBibTeX XMLCite \textit{J. Smith-Roberge} et al., Eur. J. Appl. Math. 30, No. 1, 196--218 (2019; Zbl 1407.92030) Full Text: DOI
Ding, Jie; Sun, Hui; Wang, Zhongming; Zhou, Shenggao Computational study on hysteresis of ion channels: multiple solutions to steady-state Poisson-Nernst-Planck equations. (English) Zbl 1488.70028 Commun. Comput. Phys. 23, No. 5, 1549-1572 (2018). MSC: 70K50 92C05 37N30 65M99 97M10 PDFBibTeX XMLCite \textit{J. Ding} et al., Commun. Comput. Phys. 23, No. 5, 1549--1572 (2018; Zbl 1488.70028) Full Text: DOI arXiv
Bates, Peter; Fusco, Giorgio; Karali, Georgia Gradient dynamics: motion near a manifold of quasi-equilibria. (English) Zbl 1409.37076 SIAM J. Appl. Dyn. Syst. 17, No. 3, 2106-2145 (2018). Reviewer: Ahmed Youssfi (Fès) MSC: 37L25 35A15 35K58 35B40 PDFBibTeX XMLCite \textit{P. Bates} et al., SIAM J. Appl. Dyn. Syst. 17, No. 3, 2106--2145 (2018; Zbl 1409.37076) Full Text: DOI
Fadai, Nabil T.; Ward, Michael J.; Wei, Juncheng A time-delay in the activator kinetics enhances the stability of a spike solution to the Gierer-Meinhardt model. (English) Zbl 1395.37055 Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1431-1458 (2018). MSC: 37N25 92E20 35K57 92C15 92C37 35Q92 PDFBibTeX XMLCite \textit{N. T. Fadai} et al., Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1431--1458 (2018; Zbl 1395.37055) Full Text: DOI
Matkowsky, B. J. Singular perturbations in noisy dynamical systems. (English) Zbl 1394.37083 Eur. J. Appl. Math. 29, No. 4, 570-593 (2018); corrigendum ibid. 29, No. 4, 594 (2018). MSC: 37H10 60J70 PDFBibTeX XMLCite \textit{B. J. Matkowsky}, Eur. J. Appl. Math. 29, No. 4, 570--593 (2018; Zbl 1394.37083) Full Text: DOI
Palanivel, J.; Suresh, K.; Premraj, D.; Thamilmaran, K. Effect of fractional-order, time-delay and noisy parameter on slow-passage phenomenon in a nonlinear oscillator. (English) Zbl 1392.37092 Chaos Solitons Fractals 106, 35-43 (2018). MSC: 37N20 94C05 34K18 PDFBibTeX XMLCite \textit{J. Palanivel} et al., Chaos Solitons Fractals 106, 35--43 (2018; Zbl 1392.37092) Full Text: DOI
Amore, Paolo Exact sum rules for quantum billiards of arbitrary shape. (English) Zbl 1382.35174 Ann. Phys. 388, 12-25 (2018). MSC: 35P20 37N20 37D50 PDFBibTeX XMLCite \textit{P. Amore}, Ann. Phys. 388, 12--25 (2018; Zbl 1382.35174) Full Text: DOI arXiv
Kuehn, Christian Uncertainty transformation via Hopf bifurcation in fast-slow systems. (English) Zbl 1404.37063 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2200, Article ID 20160346, 17 p. (2017). MSC: 37H20 34C23 34E13 PDFBibTeX XMLCite \textit{C. Kuehn}, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2200, Article ID 20160346, 17 p. (2017; Zbl 1404.37063) Full Text: DOI arXiv
Visser, S.; Nicks, R.; Faugeras, O.; Coombes, S. Standing and travelling waves in a spherical brain model: the Nunez model revisited. (English) Zbl 1376.92014 Physica D 349, 27-45 (2017). MSC: 92C20 45K05 45M10 37N25 92C55 PDFBibTeX XMLCite \textit{S. Visser} et al., Physica D 349, 27--45 (2017; Zbl 1376.92014) Full Text: DOI
Moyles, Iain R.; Ward, Michael J. Existence, stability, and dynamics of ring and near-ring solutions to the saturated Gierer-Meinhardt model in the semistrong regime. (English) Zbl 1434.35017 SIAM J. Appl. Dyn. Syst. 16, No. 1, 597-639 (2017). MSC: 35K40 35B25 35B32 35B36 35B40 35K57 35P30 37M20 PDFBibTeX XMLCite \textit{I. R. Moyles} and \textit{M. J. Ward}, SIAM J. Appl. Dyn. Syst. 16, No. 1, 597--639 (2017; Zbl 1434.35017) Full Text: DOI
Premraj, D.; Suresh, K.; Banerjee, Tanmoy; Thamilmaran, K. An experimental study of slow passage through Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator. (English) Zbl 1473.37064 Commun. Nonlinear Sci. Numer. Simul. 37, 212-221 (2016). MSC: 37G15 PDFBibTeX XMLCite \textit{D. Premraj} et al., Commun. Nonlinear Sci. Numer. Simul. 37, 212--221 (2016; Zbl 1473.37064) Full Text: DOI
Gambino, G.; Lombardo, M. C.; Lupo, S.; Sammartino, M. Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion. (English) Zbl 1361.35086 Ric. Mat. 65, No. 2, 449-467 (2016). MSC: 35K57 35B32 37L10 PDFBibTeX XMLCite \textit{G. Gambino} et al., Ric. Mat. 65, No. 2, 449--467 (2016; Zbl 1361.35086) Full Text: DOI arXiv
Yang, Rui; Song, Yongli Spatial resonance and Turing-Hopf bifurcations in the Gierer-Meinhardt model. (English) Zbl 1344.37061 Nonlinear Anal., Real World Appl. 31, 356-387 (2016). MSC: 37G10 92C15 35K57 35B32 37M05 PDFBibTeX XMLCite \textit{R. Yang} and \textit{Y. Song}, Nonlinear Anal., Real World Appl. 31, 356--387 (2016; Zbl 1344.37061) Full Text: DOI
Sewalt, L.; Doelman, A.; Meijer, H. G. E.; Rottschäfer, V.; Zagaris, A. Tracking pattern evolution through extended center manifold reduction and singular perturbations. (English) Zbl 1364.35040 Physica D 298-299, 48-67 (2015). MSC: 35B36 35K57 37D45 37G10 PDFBibTeX XMLCite \textit{L. Sewalt} et al., Physica D 298--299, 48--67 (2015; Zbl 1364.35040) 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
Mangioni, Sergio E. Interaction between “Dissipative solitons” stabilized by aggregation in excitable kinetics. (English) Zbl 1515.92058 Eur. Phys. J. B, Condens. Matter Complex Syst. 87, No. 10, Paper No. 248, 8 p. (2014). MSC: 92D25 37N25 35C08 PDFBibTeX XMLCite \textit{S. E. Mangioni}, Eur. Phys. J. B, Condens. Matter Complex Syst. 87, No. 10, Paper No. 248, 8 p. (2014; Zbl 1515.92058) Full Text: DOI
Horikawa, Yo Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons. (English) Zbl 1323.92014 Neural Netw. 53, 26-39 (2014). MSC: 92B20 37N25 92C20 PDFBibTeX XMLCite \textit{Y. Horikawa}, Neural Netw. 53, 26--39 (2014; Zbl 1323.92014) Full Text: DOI
You, Yuncheng Random attractor for stochastic reversible Schnackenberg equations. (English) Zbl 1332.37059 Discrete Contin. Dyn. Syst., Ser. S 7, No. 6, 1347-1362 (2014). Reviewer: Hans Crauel (Frankfurt am Main) MSC: 37L55 37L30 35B40 35K55 60H15 PDFBibTeX XMLCite \textit{Y. You}, Discrete Contin. Dyn. Syst., Ser. S 7, No. 6, 1347--1362 (2014; Zbl 1332.37059) Full Text: DOI
Horikawa, Yo Metastable and chaotic transient rotating waves in a ring of unidirectionally coupled bistable Lorenz systems. (English) Zbl 1417.37126 Physica D 261, 8-18 (2013). MSC: 37D45 37E10 PDFBibTeX XMLCite \textit{Y. Horikawa}, Physica D 261, 8--18 (2013; Zbl 1417.37126) Full Text: DOI
Wang, Weiming; Cai, Yongli; Zhu, Yanuo; Guo, Zhengguang Allee-effect-induced instability in a reaction-diffusion predator-prey model. (English) Zbl 1272.37038 Abstr. Appl. Anal. 2013, Article ID 487810, 10 p. (2013). MSC: 37N25 92D25 35Q92 PDFBibTeX XMLCite \textit{W. Wang} et al., Abstr. Appl. Anal. 2013, Article ID 487810, 10 p. (2013; Zbl 1272.37038) Full Text: DOI
Lucarini, Valerio; Faranda, Davide; Wouters, Jeroen Universal behaviour of extreme value statistics for selected observables of dynamical systems. (English) Zbl 1254.60050 J. Stat. Phys. 147, No. 1, 63-73 (2012). Reviewer: Wiesław Dziubdziela (Kielce) MSC: 60G70 37A50 PDFBibTeX XMLCite \textit{V. Lucarini} et al., J. Stat. Phys. 147, No. 1, 63--73 (2012; Zbl 1254.60050) Full Text: DOI arXiv
Levy, Chris; Iron, David Model of cell signal transduction in a three-dimensional domain. (English) Zbl 1232.92045 J. Math. Biol. 63, No. 5, 831-854 (2011). MSC: 92C37 92C40 35K57 35B25 65C20 37N25 PDFBibTeX XMLCite \textit{C. Levy} and \textit{D. Iron}, J. Math. Biol. 63, No. 5, 831--854 (2011; Zbl 1232.92045) Full Text: DOI
Horikawa, Yo; Kitajima, Hiroyuki Bifurcation and stabilization of oscillations in ring neural networks with inertia. (English) Zbl 1180.37128 Physica D 238, No. 23-24, 2409-2418 (2009). MSC: 37N25 92C20 PDFBibTeX XMLCite \textit{Y. Horikawa} and \textit{H. Kitajima}, Physica D 238, No. 23--24, 2409--2418 (2009; Zbl 1180.37128) Full Text: DOI
Ricard, M. R.; Mischler, S. Turing instabilities at Hopf bifurcation. (English) Zbl 1188.35104 J. Nonlinear Sci. 19, No. 5, 467-496 (2009). Reviewer: Yuri V. Rogovchenko (Umeå) MSC: 35K57 34C29 37G15 PDFBibTeX XMLCite \textit{M. R. Ricard} and \textit{S. Mischler}, J. Nonlinear Sci. 19, No. 5, 467--496 (2009; Zbl 1188.35104) 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
van Heijster, Peter; Doelman, Arjen; Kaper, Tasso J. Pulse dynamics in a three-component system: Stability and bifurcations. (English) Zbl 1153.37437 Physica D 237, No. 24, 3335-3368 (2008). MSC: 37L10 37L15 35K57 35B32 35B35 PDFBibTeX XMLCite \textit{P. van Heijster} et al., Physica D 237, No. 24, 3335--3368 (2008; Zbl 1153.37437) Full Text: DOI
Felmer, Patricio; Martínez, Salomé; Tanaka, Kazunaga Highly oscillatory behavior of the activator in the Gierer and Meinhardt system. (English) Zbl 1173.37010 Math. Ann. 340, No. 4, 749-773 (2008). Reviewer: Antonio Bove (Bologna) MSC: 37B25 35J60 35J55 34B15 PDFBibTeX XMLCite \textit{P. Felmer} et al., Math. Ann. 340, No. 4, 749--773 (2008; Zbl 1173.37010) Full Text: DOI Link
Maini, Philip K.; Wei, Juncheng; Winter, Matthias Stability of spikes in the shadow Gierer-Meinhardt system with robin boundary conditions. (English) Zbl 1163.37348 Chaos 17, No. 3, 037106, 16 p. (2007). MSC: 37D45 PDFBibTeX XMLCite \textit{P. K. Maini} et al., Chaos 17, No. 3, 037106, 16 p. (2007; Zbl 1163.37348) Full Text: DOI Link
Iron, D.; Rumsey, J. Stability of asymmetric spike solutions to the Gierer-Meinhardt system. (English) Zbl 1163.37337 Chaos 17, No. 3, 037105, 17 p. (2007). MSC: 37D45 PDFBibTeX XMLCite \textit{D. Iron} and \textit{J. Rumsey}, Chaos 17, No. 3, 037105, 17 p. (2007; Zbl 1163.37337) Full Text: DOI Link
Burke, John; Knobloch, Edgar Homoclinic snaking: Structure and stability. (English) Zbl 1163.37317 Chaos 17, No. 3, 037102, 15 p. (2007). MSC: 37D45 PDFBibTeX XMLCite \textit{J. Burke} and \textit{E. Knobloch}, Chaos 17, No. 3, 037102, 15 p. (2007; Zbl 1163.37317) Full Text: DOI Link
Otto, Felix; Reznikoff, Maria G. Slow motion of gradient flows. (English) Zbl 1138.35036 J. Differ. Equations 237, No. 2, 372-420 (2007). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K55 35B35 37L15 PDFBibTeX XMLCite \textit{F. Otto} and \textit{M. G. Reznikoff}, J. Differ. Equations 237, No. 2, 372--420 (2007; Zbl 1138.35036) Full Text: DOI
Potapov, A. B.; Hillen, T. Metastability in chemotaxis models. (English) Zbl 1170.35460 J. Dyn. Differ. Equations 17, No. 2, 293-330 (2005). MSC: 35K57 37L10 92C17 PDFBibTeX XMLCite \textit{A. B. Potapov} and \textit{T. Hillen}, J. Dyn. Differ. Equations 17, No. 2, 293--330 (2005; Zbl 1170.35460) Full Text: DOI
Chen, Xinfu Generation, propagation, and annihilation of metastable patterns. (English) Zbl 1061.35014 J. Differ. Equations 206, No. 2, 399-437 (2004). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B25 35K57 37L99 74N99 PDFBibTeX XMLCite \textit{X. Chen}, J. Differ. Equations 206, No. 2, 399--437 (2004; Zbl 1061.35014) Full Text: DOI
Kalies, William D.; VanderVorst, Robert C. A. M.; Wanner, Thomas Slow motion in higher-order systems and \(\Gamma\)-convergence in one space dimension. (English) Zbl 0976.35005 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 1, 33-57 (2001). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K60 35A15 37C29 PDFBibTeX XMLCite \textit{W. D. Kalies} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 1, 33--57 (2001; Zbl 0976.35005) Full Text: DOI
Bates, Peter W.; Fusco, Giorgio Equilibria with many nuclei for the Cahn-Hilliard equation. (English) Zbl 0990.35016 J. Differ. Equations 160, No. 2, 283-356 (2000). Reviewer: Michael Grinfeld (Glasgow) MSC: 35B25 35K35 35K55 35B05 37N15 PDFBibTeX XMLCite \textit{P. W. Bates} and \textit{G. Fusco}, J. Differ. Equations 160, No. 2, 283--356 (2000; Zbl 0990.35016) Full Text: DOI