Criteria of the Existence of Moving Structures in Two-Component Reaction-Diffusion Systems

Abstract

The conditions of propagating and non-propagating structures in two-component reaction-diffusion systems with τ_p /τ_s “ 1 and ℓ_pℓ_s ” 1 (where τ_p,τ_s are characteristic relaxationtimes, and ℓ_pℓ_s are cha characteristic diffusion lengths of subsystems) are considered theoretically. The model with piece-wise linear sources was used to show that ratio V_p/V_s (where V_p=ℓ_p/τ_p, V_s=ℓ_s/τ_s are characteristic velocities of subsystems) is a bifurcation parameter, which determines whether propagating or non-proapgating structures exist or not. In this model stable non-propagating structures occur only if v_p /v_s < 1. Otherwise (v_p/v_s > 1) the propagating stable structures arise and the non-propagating ones loose their stability.