\(1:3\) resonance and chaos in a discrete Hindmarsh-Rose model. (English) Zbl 1442.37101

Summary: \(1:3\) resonance of a two-dimensional discrete Hindmarsh-Rose model is discussed by normal form method and bifurcation theory. Numerical simulations are presented to illustrate the theoretical analysis, which predict the occurrence of a closed invariant circle, period-three saddle cycle, and homoclinic structure. Furthermore, it also displays the complex dynamical behaviors, especially the transitions between three main dynamical behaviors, namely, quiescence, spiking, and bursting.


37N25 Dynamical systems in biology
92C20 Neural biology
Full Text: DOI


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