Dynamics in the Parameter Space of a Neuron Model

Some two-dimensional parameter-space diagrams are numerically obtained by considering the largest Lyapunov exponent for a four-dimensional thirteen-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and it is shown that depending on the combination of parameters, a typical scenario can be preserved: for some choice of two parameters, the parameter plane presents a comb-shaped chaotic region embedded in a large periodic region. It is also shown that there exist regions close to these comb-shaped chaotic regions, separated by the comb teeth, organizing themselves in period-adding bifurcation cascades.