Stationary pattern formation in a discrete excitable system with strong inhibitory coupling

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 May;79(5 Pt 2):056203. doi: 10.1103/PhysRevE.79.056203. Epub 2009 May 5.

Abstract

We study a discrete model described by coupled excitable elements following the monostable FitzHugh-Nagumo equations. Our model has a weakly coupled activator and a strongly coupled inhibitor. For two-coupled excitable elements, we show that the trivial state always exists stably, while nontrivial stable states appear depending on the coupling strengths. In a one-dimensional array, only the elements near the initial condition step remain at nontrivial states. We discuss stationary pattern formation in a one-dimensional array and a two-dimensional lattice using the analytical results of a two-coupled system.

Publication types

  • Research Support, Non-U.S. Gov't