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

van Heijster, Peter & Sandstede, Bjorn (2012) Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system. RIMS Kokyuroku Bessatsu, B31, pp. 135-155.

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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 stabil-ity 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.

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ID Code: 55959
Item Type: Journal Article
Refereed: Yes
Additional URLs:
ISSN: 1881-6193
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Research Institute for Mathematical Sciences (RIMS)
Deposited On: 21 Dec 2012 01:01
Last Modified: 12 Jun 2013 15:24

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