Onset of unidirectional pulse propagation in an excitable medium with asymmetric heterogeneity

Takashi Teramoto, Xiaohui Yuan, Markus Bär, Yasumasa Nishiura

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Heterogeneity is one of the most important and ubiquitous types of external perturbations in dissipative systems. To know the behaviors of pulse waves in such media is closely related to studying the collision process between the pulse and the heterogeneity-induced-ordered pattern. In particular, we focus on unidirectional propagation of pulses in a medium with an asymmetric bump heterogeneity. This topic has attracted much interest recently with respect to potential computational aspects of chemical pulse propagation as well as with respect to pulse propagation in biological signal processing. We employ a three-component reaction-diffusion system with one activator and two inhibitor species to illustrate these issues. The reduced dynamics near a drift bifurcation describes the phenomena in the full partial differential equations by ordinary differential equations. Such a reduced dynamics is able to capture unidirectional propagation properties of pulses near an asymmetric heterogeneity in a qualitatively correct way. A remarkable feature is that such unidirectional behavior is linked to the imperfection of global bifurcation structure and the resulting asymmetric locations of critical points.

Original languageEnglish
Article number046205
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number4
DOIs
Publication statusPublished - 2009 Apr 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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