Control of spiral wave and turbulence in the time-varied reaction-diffusion system

Abstract

We investigated the external electric field-induced transition of the spiral wave and turbulence in a class of time-varied reaction-diffusion systems. In our numerical simulation, a modified Fitzhugh-Nagumo model, which was used to describe the excitable and/or oscillatory media under appropriate parameters, was investigated. The effect induced by the random and/or other uncertain factors (for example, external and interior noise, gas pressure, temperature gradient and deformation of media etc.) was considered. The amplitude of the fluctuations of parameters was selected at appropriate values so that stable rotating spiral wave, meandering spiral wave and turbulence could be observed respectively. The external electric field was introduced into the media after a transient period allowing for parameter fluctuations. It was found that only the breakup of spiral wave was observed and the whole media could not reach homogeneous state when weak electric field and parameter fluctuation were used. It was confirmed that the breakup of spiral wave happens and then the whole media becomes stably homogeneous when appropriately strong intensity of external electric field is applied to the whole media together with the action of parameter fluctuation. The snapshots of the activator are used to investigate the transition of the patterns in the presence of external electric field and under parameter fluctuation, and relevant theoretical discussion is given in the precent paper.