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

Sehgal, Sucheta; Foulkes, Andrew J.

doi:10.1103/physreve.102.012212

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2024

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Cited by 5 publications

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“…Note, that the similar hysteresis phenomenon was recently observed in the context of the Barkley model within the bistability region [25]. Moreover, a hysteresis phenomenon has been described in context of the FitzHugh-Nagumo model [28,29].…”

Section: Discussionsupporting

confidence: 76%

Two Domains of Meandering Spiral Waves in a Modified Barkley Model

Zykov

Bodenschatz

2022

Front. Appl. Math. Stat.

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The stability of rigidly rotating spiral waves is a very important topic in the study of nonlinear reaction-diffusion media. Computer experiments carried out with a slightly modified Barkley model showed that, in addition to one region of instability observed earlier in the original Barkley model, there is another one exhibiting completely different properties. The wave instability in the second region is not related to the Hopf bifurcation. Moreover, hysteresis effects are observed at the boundary of the region. This means that in the vicinity of this region of instability, direct integration of the model equations leads either to a rigidly rotating or meandering spiral, depending on the initial conditions.

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Section: Discussionsupporting

confidence: 76%