A lattice Boltzmann based local feedback control approach for spiral wave

Suppression of spiral wave attracts more and more attention in nonlinear systems. In this paper, a spiral wave local feedback control approach based on the FitzHugh-Nagumo (FHN) model is studied with lattice Boltzmann method. Numerical simulations are performed to investigate the effects of initial conditions for the spiral wave formation, model parameters, size and position of the feedback control region, and feedback control parameters on the behavior of spiral wave. The results show that there are three characteristics of spiral wave elimination. The first is that initial conditions of the spiral wave formation have little influence on feedback control of spiral wave. Secondly, the model parameters are related to the time needed for the elimination of spiral wave, for example, the larger the mutual time scales, the faster the elimination of spiral wave. Finally, through selecting the size and position of the feedback region, spiral wave can be effectively removed with weak feedback signal.