Reaction—Diffusion Systems and Interface Dynamics
Existing studies on reaction—diffusion systems have been carried out with the Belousov-Zhabotinskii reaction acting as the standard example. Approaches based on amplitude equations are in general not suited to describe patterns peculiar to such ‘excitable’ systems because, while excitability originates in a particular property of global flow in phase space, amplitude equations are obtained by considering only local flow. In fact, BZ reaction systems display wave patterns that lack both the temporal and spatial smoothness displayed by solutions to amplitude equations, and thus it is much more natural to treat excitable systems using local interface structure representing the sudden change in state of a system over a small distance. Patterns containing interfaces arise out of the cooperative dynamics of degrees of freedom undergoing rapid and slow temporal change. Rapidly changing degrees of freedom form a bistable partial subsystem consisting of two states, an active (or excitable) state and an inactive (or nonexcitable) state. The speed with which the transition between these two states is carried out is controlled by the slowly changing degrees of freedom.
KeywordsPropagation Speed Spiral Wave Phase Field Model Amplitude Equation Excitable System
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