Frozen state of spiral waves in excitable media

Abstract

It has long been observed in experiments that frozen state of spiral waves can spontaneously appear in both excitable and oscillatory media, in which several spiral waves coexist and are well separated by thin walls (shocks). In this work, we study the global structure of frozen state of spiral waves in excitable media and find that different from stationary shocks in oscillatory media, in excitable media the shock dynamics actually depends on the status of single spiral, which is also determined by the system parameter, i.e., the shock line can be stationary if the single spiral is rigidly rotating, whereas it can wiggle if the single spiral is meandering, and the wiggling amplitude increases with the degree of meandering. We also find the stationary structure of shock line can still be well predicted by a previous theory, which has been developed for the frozen state of spiral waves in oscillatory media. All these findings are generic and expected to be verified in experiments.