Two Domains of Meandering Spiral Waves in a Modified Barkley Model

Frontiers in Applied Mathematics and Statistics

Eberhard Bodenschatz³  Vladimir Zykov⁴ 

[1] German Center for Cardiovascular Research, Partner Site Göttingen, Göttingen, Germany;Institute for the Dynamics of Complex Systems, Georg-August-University Göttingen, Göttingen, Germany;Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, United States;Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany;

关键词: excitable media;    spiral wave;    instability;    hysteresis;    modified Barkley model;   

DOI  :  10.3389/fams.2022.903563

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown