Abstract
In this paper, nonlinear dynamic behaviors of a Hindmarsh-Rose (HR) neuron model are investigated through discrete mapping method. Periodic and chaotic firing motions are observed of the system with different external excitation. Stability boundaries in terms of the external excitation are predicted by the eigenvalues of the global mappings. A nonlinear analog circuit is developed on circuit simulations for the verification of the various firing patterns of the HR neuron model. A route from periodic firing activity to chaotic firing are observed in simulation and confirmed by the theoretical research. Time series for the potential of numerical model and circuit model are presented. The evolution processes of the routes into and out of chaotic firing activities are revealed.
