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The stability of stationary fronts for a discrete nerve axon model
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[1] |
H. J. Hupkes, L. Morelli. Travelling corners for spatially discrete reaction-diffusion systems. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1609-1667. doi: 10.3934/cpaa.2020058 |
[2] |
Ana Carpio, Gema Duro. Explosive behavior in spatially discrete reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 693-711. doi: 10.3934/dcdsb.2009.12.693 |
[3] |
Hiroshi Matsuzawa. On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous environments. Conference Publications, 2009, 2009 (Special) : 516-525. doi: 10.3934/proc.2009.2009.516 |
[4] |
Wei-Jie Sheng, Wan-Tong Li. Multidimensional stability of time-periodic planar traveling fronts in bistable reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2681-2704. doi: 10.3934/dcds.2017115 |
[5] |
Jacson Simsen, Mariza Stefanello Simsen, Marcos Roberto Teixeira Primo. Reaction-Diffusion equations with spatially variable exponents and large diffusion. Communications on Pure and Applied Analysis, 2016, 15 (2) : 495-506. doi: 10.3934/cpaa.2016.15.495 |
[6] |
Masaharu Taniguchi. Instability of planar traveling waves in bistable reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 21-44. doi: 10.3934/dcdsb.2003.3.21 |
[7] |
Henri Berestycki, Nancy Rodríguez. A non-local bistable reaction-diffusion equation with a gap. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 685-723. doi: 10.3934/dcds.2017029 |
[8] |
Maho Endo, Yuki Kaneko, Yoshio Yamada. Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3375-3394. doi: 10.3934/dcds.2020033 |
[9] |
Masaharu Taniguchi. Multi-dimensional traveling fronts in bistable reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 1011-1046. doi: 10.3934/dcds.2012.32.1011 |
[10] |
Masaharu Taniguchi. Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3981-3995. doi: 10.3934/dcds.2020126 |
[11] |
Michio Urano, Kimie Nakashima, Yoshio Yamada. Transition layers and spikes for a reaction-diffusion equation with bistable nonlinearity. Conference Publications, 2005, 2005 (Special) : 868-877. doi: 10.3934/proc.2005.2005.868 |
[12] |
François Hamel, Jean-Michel Roquejoffre. Heteroclinic connections for multidimensional bistable reaction-diffusion equations. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 101-123. doi: 10.3934/dcdss.2011.4.101 |
[13] |
Zhao-Xing Yang, Guo-Bao Zhang, Ge Tian, Zhaosheng Feng. Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 581-603. doi: 10.3934/dcdss.2017029 |
[14] |
Yangyang Shi, Hongjun Gao. Homogenization for stochastic reaction-diffusion equations with singular perturbation term. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2401-2426. doi: 10.3934/dcdsb.2021137 |
[15] |
Guangying Lv, Jinlong Wei, Guang-an Zou. Noise and stability in reaction-diffusion equations. Mathematical Control and Related Fields, 2022, 12 (1) : 147-168. doi: 10.3934/mcrf.2021005 |
[16] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, 2021, 29 (4) : 2599-2618. doi: 10.3934/era.2021003 |
[17] |
Peter Howard, K. Zumbrun. The Evans function and stability criteria for degenerate viscous shock waves. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 837-855. doi: 10.3934/dcds.2004.10.837 |
[18] |
Ramon Plaza, K. Zumbrun. An Evans function approach to spectral stability of small-amplitude shock profiles. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 885-924. doi: 10.3934/dcds.2004.10.885 |
[19] |
Wei Wang, Anthony Roberts. Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 253-273. doi: 10.3934/dcds.2011.31.253 |
[20] |
Jong-Shenq Guo, Yoshihisa Morita. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 193-212. doi: 10.3934/dcds.2005.12.193 |
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