Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh–Rose neuron model

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two- dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the determin- istic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in dif- ferent two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh-Rose neuron model

chaos, neural firing, bifurcation, Hindmarsh-Rose model