Abstract
In this work, the properties of several types of asymptotic solutions of a two-dimensional reaction–diffusion system with the FitzHugh–Nagumo model were studied. When several asymptotic solutions coexist in a parameter region around the bifurcation point, there is a possibility of producing the locally connecting bistable solution (LCBS). The dynamic LCBS (d-LCBS) obtained in the present study consists of two domains, the static stripe pattern and the periodically fluctuating one. It is clarified that the nearly equal stability of two global asymptotic solutions and the complete synchronization at the boundary are needed to produce the d-LCBSs. Furthermore, the dependence of the stability of solutions on the extent of the computing domain was also investigated.
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