Effect of Electrical and Chemical Autapse on the Firing Pattern and Synchronization of the Rulkov Neuron Model

The Rulkov map model is an efficient model for reproducing different dynamics of the neurons. In specific neurons, the electrical activity is regulated by time-delayed self-feedback called autapse. This paper investigates how the dynamics of the Rulkov model change by considering the autaptic current. Both electrical and chemical autapses are considered, and bifurcation diagrams are plotted for different autapse gains and time delays. Consequently, various firing patterns of the model are illustrated. The results represent that the firing pattern is greatly dependent on the values of autapse parameters. Moreover, the average firing frequency is computed and it is shown that the enhanced firing activity is induced by the inhibitory autapse. The synchronous dynamics of coupled Rulkov maps in the presence of autapse is also studied. It is shown that the electrical autapse enhances synchronization in small time delays, while the enhancement is achieved by chemical autapse in any time delay. However, increasing the time delay reduces the synchronization region.