(Investigating a chaotic bursting model near saddle-focus homoclinic orbit bifurcation (Shilnikov Bifurcation

In this paper, we investigate a model which is a fast-slow burster of the ”1+2” type. By this model, we are able to model some the actions and reactions in the neural cells. We study the dynamical behavior of this model and its reactions to the changes in the controllers (I,µ,ω). Using mathematical techniques, we show that the model undergoes the saddle-focus homoclinic orbit (SFHO) or Shilnikov bifurcation. In addition, we show that the system has a chaotic burst mode. We consider three parameters I,µ, and ω as controllers for the system and study their effects in the system separately. In the following, we show how to control the Burst Duration, Interburst Interval and Period of bursting by controlling these parameters. Moreover, we show that the I and µ have more influence on the chaos, Burst Duration and Period of Bursting and ω controls the number of spikes in any burst better