Two Domains of Meandering Spiral Waves in a Modified Barkley Model

Zykov, Vladimir S.; Bodenschatz, Eberhard

doi:10.3389/fams.2022.903563

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Two Domains of Meandering Spiral Waves in a Modified Barkley Model

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Zykov, Vladimir S.
Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Bodenschatz, Eberhard
Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Zykov, V. S., & Bodenschatz, E. (2022). Two Domains of Meandering Spiral Waves in a Modified Barkley Model. Frontiers in Applied Mathematics and Statistics, 8: 903563, pp. 1. doi:10.3389/fams.2022.903563.

Cite as: https://hdl.handle.net/21.11116/0000-000A-711C-8

Abstract

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.