Interaction and breakup of inwardly rotating spiral waves in an inhomogeneous oscillatory medium

We studied the effects of spatial inhomogeneities on inwardly rotating spiral waves in a typical type of oscillatory medium using the complex-Ginzburg-Landau equation. With a small degree of the inhomogeneity in the medium, the slower inward spiral always suppressed a faster spiral; when the inhomogeneity exceeded a critical value, however, a transition occurred to the coexistence of multiple inward spirals, insulated by regions of highly disordered wave break. The occurrence of this transition is examined theoretically and shown to be due to the Eckhaus instability.