McKean caricature of the FitzHugh-Nagumo model: traveling pulses in a discrete diffusive medium.
作者： Arnaud Tonnelier
DOI: 10.1103/PHYSREVE.67.036105
关键词:
摘要: This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by McKean caricature FitzHugh-Nagumo model. In limit a weak coupling strength, we construct and obtain critical constant below which propagation failure occurs. We report existence two different pulse waves with speeds. Analytical results on speed obtained. Earlier in bistable medium found as limiting regime our analysis.
archives-ouvertes.fr
harvard.edu
sci-hub.se 参考文章(22)
Peter Grindrod, Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations ,(1991)
James Keener, James Sneyd, Mathematical physiology ,(1998)
Gil Bub, Alvin Shrier, Leon Glass, Spiral wave generation in heterogeneous excitable media. Physical Review Letters. ,vol. 88, pp. 058101- ,(2002) , 10.1103/PHYSREVLETT.88.058101
James P. Keener, Propagation and its failure in coupled systems of discrete excitable cells Siam Journal on Applied Mathematics. ,vol. 47, pp. 556- 572 ,(1987) , 10.1137/0147038
Bertram Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation Journal of Differential Equations. ,vol. 96, pp. 1- 27 ,(1992) , 10.1016/0022-0396(92)90142-A
Thomas Erneux, Grégoire Nicolis, Propagating waves in discrete bistable reaction-diffusion systems Physica D: Nonlinear Phenomena. ,vol. 67, pp. 237- 244 ,(1993) , 10.1016/0167-2789(93)90208-I
Gábor Fáth, Propagation failure of traveling waves in a discrete bistable medium arXiv: Pattern Formation and Solitons. ,(1997) , 10.1016/S0167-2789(97)00251-0
Avijit Lahiri, Priyadarshi Majumdar, Mahendra Sinha Roy, Traveling kinks in discrete media: exact solution in a piecewise linear model. Physical Review E. ,vol. 65, pp. 026106- ,(2002) , 10.1103/PHYSREVE.65.026106
A. Carpio, L. Bonilla, Wave Front Depinning Transition in Discrete One-Dimensional Reaction-Diffusion Systems Physical Review Letters. ,vol. 86, pp. 6034- 6037 ,(2001) , 10.1103/PHYSREVLETT.86.6034
A.R.A. ANDERSON, B.D. SLEEMAN, WAVE FRONT PROPAGATION AND ITS FAILURE IN COUPLED SYSTEMS OF DISCRETE BISTABLE CELLS MODELLED BY FITZHUGH-NAGUMO DYNAMICS International Journal of Bifurcation and Chaos. ,vol. 05, pp. 63- 74 ,(1995) , 10.1142/S0218127495000053