Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

doi:10.1088/1674-1056/19/10/100509

Abstract This paper theoretically analyses and studies stationary patterns in diffusively coupled bistable elements. Since these stationary patterns consist of two types of stationary mode structure: kink and pulse, a mode analysis method is proposed to approximate the solutions of these localized basic modes and to analyse their stabilities. Using this method, it reconstructs the whole stationary patterns. The cellular mode structures (kink and pulse) in bistable media fundamentally differ from stationary patterns in monostable media showing spatial periodicity induced by a diffusive Turing bifurcation.

Keywords: discrete reaction–diffusion system stationary patterns bistable mode analysis

Received: 18 January 2010
Revised: 09 April 2010
Accepted manuscript online:

PACS:	02.30.Oz	(Bifurcation theory)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project partially supported by the Outstanding Oversea Scholar Foundation of the Chinese Academy of Sciences (Bairenjihua) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

Cite this article:

Zou Wei(邹为) and Zhan Meng(占萌) Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis 2010 Chin. Phys. B 19 100509

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Stationary patterns in a discrete bistable reaction–diffusion system: mode analysis

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