Non-local coexistence of multiple spiral waves with independent frequencies

The interactions of several spiral waves with different independent rotation frequencies are studied in a model of two-dimensional complex Ginzburg–Laudau equation. We find a general coexistence phenomenon, non-local non-phase-locking-invasion coexistence, that is, the non-slowest spiral wave can survive and not be killed by the fastest spiral wave as it is insulated from the fastest one with the sacrifice of the slowest one, which stays in the spatial position between the fastest spiral and the non-slowest one. Both the parameter non-monotonicity and the non-phase-locking invasion between the fastest and the slowest spiral waves play key roles in this phenomenon. Importantly, the results could give a general idea for extensively observed coexistence of spiral waves in various inhomogeneous circumstances.