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.
"1 : 3 Resonance and Chaos in a Discrete Hindmarsh-Rose Model." J. Appl. Math. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/896478