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.