Unexplored aspects of spiral wave dynamics in the Barkley model within an extended parameter range.

Abstract

The Barkley model has been widely used to simulate diverse reaction-diffusion systems exhibiting various self-organization processes, including creation of spiral waves. Depending on the given parameters, this model is capable of simulating monostable, bistable, or oscillatory dynamics that are often observed in nature. This study is concentrated on the general features of spiral wave dynamics in the extended parameter range of the Barkley model, including both monostable and bistable dynamics. The numerical data obtained and the results of analytical studies illustrate the existence and the interplay between spiral wave dynamics in these two different but closely related regimes. In particular, the symmetry between the spiral waves in monostable and bistable regions is demonstrated, analytical expressions for the boundaries of these regions are found, the existence of the hysteresis phenomenon in the dynamics of spiral waves is discovered, and an additional region of existence of spiral waves is found in the region of a low excitability.