Synchronization of two spiral waves interacting through a passive medium

Abstract

Synchronization of two spiral waves in two-dimensional excitable systems interacting through a passive medium is studied by using the Bär model. The passive medium is composed of excitable elements. There are no couplings among these elements. The numerical results show that synchronization of spiral waves is significantly affected by the passive medium. When two subsystems have the same initial spiral waves, the passive medium can induce meander of stable spiral waves and cause spiral waves to transform into multi-spiral waves or anti-target waves. When initial spiral waves are in an asynchronization state, the synchronization and phase-synchronization between two spiral waves are established if the relevant parameters are properly chosen. In addition, the following phenomena are observed: the tips of two spiral waves repel each other, multi-spiral waves coexist, synchronized spatiotemporal pattern repeats periodically, and the two systems evolves into the resting state. Wave patterns can generally be observed in passive medium. However, passive medium can exhibit synchronous oscillation in certain circumstances. These results can help one understand the formation of spatiotemporal patterns in the cardiac system.