Dynamics of Nonlinear Wave Patternin Excitable Media

doi:10.7523/j.issn.2095-6134.2004.2.020

Abstract

Abstract:

Based on the Oregonator model portraying the famous Belousov Zhabotinsky chemical reaction,the dynamics of nonlinear wave pattern in excitable media is further consummated. Some basic problems such as existence and stability of waves are studied. By Painlevéanalysis,B?cklund transformationand pertubation method,some usual wave pattern solutions (for example, travelling wave,spiral wave,target wave,Vtype wave,scroll wave,etc) are analytically presented.By establishing new moving coordinatesystems in the neighborhood of the wave fornt,equations of motion of waves which describe the curvatureeffect of waves,are derived in the orthogonal coordinate system. In particular,lawof motion of the organizing filament along the radial and axial directions,respectively,is quantitatively obtained. It demonstrateswhether the filament expands or shrinks along the radial direction,and positively or inversely shifts alongthe axial direction. The result is in good accord with the existing experimental data. In addition,the coupled Oregonator is studied. Tyson’s conjecture that the stable homogeneous positive steady state may coexist with the stable echo wave in the coupled model is basically solved. The corresponding proof procedurepractically gives a general method in handling other similar problems.

Key words: excitable media, Oregonator, Belousov-Zhabotinsky chemical reaction, wave pattern solution, organizing filament

CLC Number:

ZHOU Tian-Shou, ZHANG Suo-Chun. Dynamics of Nonlinear Wave Patternin Excitable Media[J]. , 2004, 21(2): 276-281.

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