Numerical analysis of subcritical Hopf bifurcations in the two-dimensional FitzHugh-Nagumo model.
basic_science · Level V
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- Record sourced from PubMed, PMID 32795073.
- Also identified by DOI 10.1103/PhysRevE.102.012212.
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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.