Y. Yamazaki, S. Ohmori, “Ultradiscretization of reaction-diffusion type partial differential equations exhibiting pulse propagation”, Nanosystems: Physics, Chemistry, Mathematics, 2017, Volume 8, Issue 1,Pages <nobr>38

MATHEMATICS

Ultradiscretization of reaction-diffusion type partial differential equations exhibiting pulse propagation

Y. Yamazaki, S. Ohmori

Department of Physics, Department of Physics, School of Advanced Science and Engineering, Waseda University, Shinjuku, Tokyo 1698555, Japan

Abstract: Cellular automaton rules are derived from a set of reaction-diffusion partial differential equations by means of ultradiscretization method. The rules reproduce dynamical properties of pulse: annihilation, soliton-like preservation and periodic generation with a pacemaker.

Keywords: ultradiscretization, tropical discretization, pulse dynamics, cellular automaton, reaction-diffusion systems.

PACS: 05.90.+m, 02.90.+p

Received: 20.07.2016
Revised: 30.07.2016

Language: English

DOI: 10.17586/2220-8054-2017-8-1-38-41