Pattern Dynamics in an Excitable Reaction Diffusion System

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We have obtained the following new results on pattern dynamics in an excitable reaction diffusion system.1.In order to investigate the domain pattern in glow discharge and in nonlinear electric current of semiconductors, we have introduced a model system which is a coupled set of reaction diffusion equations for one activator and two ingibitors. This model equations have been studied by computer simulations and by an interfacial approach. We have assumued that the diffusion constant of the activator is sufficiently small while one of the inhibitors has extremely large diffusivity. We have derived the interface equation of motion in one dimension and carried out the stability analysis to obtain the bifurcation diagram of periodic excited solutions. The behavior at post-threshold has been explored by numerical simulations. By changing the parameters, we have found complicated motions of domains such as period doubling and quasiperiodic motions as well as the breathing and wiggling motions.2.We have obtained novel results by computer simulations of an excitable reaction diffusion system with one activator and one inhibitor where a uniform solution coexists with a limit cycle oscillation. Upon a collision of two propagating pulses, an oscillatory domain emerges and it emitts outgoing wave trains. In two dimensions, we have observed an automatic formation of concentric waves. Starting with a localized initial condition of the activator, we have obtained essentially the same results. The present results are qualitatively consistent with the concentric waves without any pacemaker observed experimentally in electro-hydrodynamic convection.