Effect of an autapse on the firing pattern transition in a bursting neuron

On the basis of the Hindmarsh–Rose (HR) neuron model, the dynamics of electrical activity and the transition of firing patterns induced by three types of autapses have been investigated in detail. The dynamic effect of an autapse is detected by imposing a feedback term with a specific time-delay and autaptic intensity. We found that the delayed autaptic feedback connection switches the electrical activities of the HR neuron among quiescent, periodic and chaotic firing patterns. In the case of an electrical autapse, the transition from a periodic to a chaotic state occurs depending on the specific autaptic intensity and the time-delay. The excitatory chemical autapse plays a positive role in generating and enhancing the chaotic state. A time delay could decrease and suppress the chaotic state in the case of inhibitory chemical self-connections with a proper autaptic intensity. The bifurcation diagram vs. time-delay and autaptic intensity has been extensively studied, and the time series of membrane potentials and the distribution of information entropy have also been calculated to confirm the bifurcation analysis.