Coexistence of stable spots and fronts in a three-component FitzHugh–Nagumo system

Abstract

We investigate regions of bistability between different travelling and stationary structures in a planar singularly-perturbed three-component reaction-diffusion system that arises in the context of gas discharge systems. In previous work, we delineated the existence and stability regions of stationary localized spots in this system. Here, we complement this analysis by establishing the stability regions of planar travelling fronts and stationary stripes. Taken together, these results imply that stable fronts and spots can coexist in three-component systems. Numerical simulations indicate that the stable fronts never move towards stable spots but instead move away from them. Received April 20, 201x. Revised September 11, 201x. 2000 Mathematics Subject Classification(s): 35K57, 35B35, 35B25

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Cite this paper

@inproceedings{Nishiura2011CoexistenceOS, title={Coexistence of stable spots and fronts in a three-component FitzHugh–Nagumo system}, author={Yasumasa Nishiura and Peter van Heijster and Bj{\"{o}rn Sandstede}, year={2011} }