Codimension-Two Bifurcation Analysis in Hindmarsh--Rose Model with Two Parameters

Bifurcation phenomena in a Hindmarsh--Rose neuron model are investigated. Special attention is paid to the bifurcation structures of two parameters, where codimension-two generalized-Hopf bifurcation and fold-Hopf bifurcation occur. The classification of firing patterns as well as the transition mechanism in different regions on the parameter plane are obtained.