Oscillatory pulse-front waves in a reaction-diffusion system with cross diffusion

Evgeny P. Zemskov, Mikhail A. Tsyganov, and Werner Horsthemke
Phys. Rev. E 97, 062206 – Published 12 June 2018
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Abstract

We explore traveling waves with oscillatory tails in a bistable piecewise linear reaction-diffusion system of the FitzHugh-Nagumo type with linear cross diffusion. These waves differ fundamentally from the standard simple fronts of the kink type. In contrast to kinks, the waves studied here have a complex shape profile with a front-back-front (a pulse-front) pattern. The characteristic feature of such pulse-front waves is a hybrid type of the speed diagram, which on the one hand reflects the typical dynamical behavior of the fronts in the FitzHugh-Nagumo model, related to the nonequilibrium Ising-Bloch bifurcation, and on the other hand exhibits also the solitary pulse scenario where several waves appear simultaneously with different speeds of propagation. We describe analytically the wave profiles and heteroclinic trajectories in the phase plane and discuss their morphology and transformation. The phenomena of wave formation and propagation are also studied by numerical simulations of the model partial differential equations. These simulations support the view that the pulse-front waves are constructed of fronts and pulses.

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  • Received 4 April 2018

DOI:https://doi.org/10.1103/PhysRevE.97.062206

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Evgeny P. Zemskov1,*, Mikhail A. Tsyganov2,†, and Werner Horsthemke3,‡

  • 1Federal Research Center for Computer Science and Control, Russian Academy of Sciences, Vavilova 40, 119333 Moscow, Russia
  • 2Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya 3, 142290 Pushchino, Moscow Region, Russia
  • 3Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA

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Issue

Vol. 97, Iss. 6 — June 2018

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