Numerical analysis of subcritical Hopf bifurcations in the two-dimensional FitzHugh-Nagumo model

Sehgal, S and Foulkes, A.J. (2020) Numerical analysis of subcritical Hopf bifurcations in the two-dimensional FitzHugh-Nagumo model. Physical Review E, 102 (1). ISSN 1550-2376 (Accepted for Publication)

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Abstract

It had been shown that the transition from a rigidly rotating spiral wave to a meandering spiral wave is via a Hopf bifurcation. Many studies have shown that these bifurcations are supercritical, but, by using simulations in a comoving frame of reference, we present numerical results which show that subcritical bifurcations are also present within FitzHugh-Nagumo. We show that a hysteresis region is present at the boundary of the rigidly rotating spiral waves and the meandering spiral waves for a particular set of parameters, a feature of FitzHugh-
Nagumo that has previously not been reported. Furthermore, we present a evidence that this bifurcation is highly sensitive to initial conditions, and it is possible to convert one solution in the hysteresis loop to the other.

Item Type: Article
Additional Information and Comments: This article has been accepted for publication in Physical Review E, published by the American Physical Society. It is made available under under a Creative Commons CC-BY 4.0 International license. The final version is available at: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.012212
Keywords: Dynamical Systems, Bifurcations, Hopf Bifurcations, Numerical Analysis, Spiral Waves, Reaction-Diffusion
Faculty / Department: Faculty of Science > Mathematics and Computer Science
Depositing User: Andrew Foulkes
Date Deposited: 14 Jul 2020 13:23
Last Modified: 21 Jul 2020 09:27
URI: https://hira.hope.ac.uk/id/eprint/3103

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