1 : 3 Resonance and Chaos in a Discrete Hindmarsh-Rose Model

Abstract EN

1 : 3 resonance of a two-dimensional discrete Hindmarsh-Rose model isdiscussed by normal form method and bifurcation theory.

Numerical simulations are presented toillustrate the theoretical analysis, which predict the occurrence of a closed invariant circle, period-threesaddle cycle, and homoclinic structure.

Furthermore, it also displays the complex dynamicalbehaviors, especially the transitions between three main dynamical behaviors, namely, quiescence,spiking, and bursting.