Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments.

作者: J. C. Comte , S. Morfu , P. Marquié

DOI: 10.1103/PHYSREVE.64.027102

关键词: Reaction–diffusion systemSystems theoryDissipative systemWavefrontBistabilityLattice (order)Front propagationPhysicsNonlinear systemStatistical physics

摘要: Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which can occur as function nonlinearity threshold parameter. Our predictions are confirmed by numerical simulations experimental results on equivalent electrical diffusive lattice.

参考文章(18)
Alwyn C. Scott, The electrophysics of a nerve fiber Reviews of Modern Physics. ,vol. 47, pp. 487- 533 ,(1975) , 10.1103/REVMODPHYS.47.487
James P. Keener, The effects of discrete gap junction coupling on propagation in myocardium Journal of Theoretical Biology. ,vol. 148, pp. 49- 82 ,(1991) , 10.1016/S0022-5193(05)80465-5
M. deCastro, E. Hofer, A. P. Muñuzuri, M. Gómez-Gesteira, G. Plank, I. Schafferhofer, V. Pérez-Muñuzuri, V. Pérez-Villar, Comparison between the role of discontinuities in cardiac conduction and in a one-dimensional hardware model. Physical Review E. ,vol. 59, pp. 5962- 5969 ,(1999) , 10.1103/PHYSREVE.59.5962
P.C. Bressloff, G. Rowlands, Exact travelling wave solutions of an “integrable” discrete reaction-diffusion equation Physica D: Nonlinear Phenomena. ,vol. 106, pp. 255- 269 ,(1997) , 10.1016/S0167-2789(97)00047-X
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
Victoria Booth, Thomas Erneux, Mechanisms for propagation failure in discrete reaction-diffusion systems Physica A-statistical Mechanics and Its Applications. ,vol. 188, pp. 206- 209 ,(1992) , 10.1016/0378-4371(92)90267-T
Victoria Booth, Thomas Erneux, Jean-Pierre Laplante, Experimental and numerical study of weakly coupled bistable chemical reactors The Journal of Physical Chemistry. ,vol. 98, pp. 6537- 6540 ,(1994) , 10.1021/J100077A019
J.P. Laplante, T. Erneux, Propagation failure and multiple steady states in an array of diffusion coupled flow reactors Physica A-statistical Mechanics and Its Applications. ,vol. 188, pp. 89- 98 ,(1992) , 10.1016/0378-4371(92)90256-P