Bifurcation and Chaos in the Cardiac Pacemaker Device Modeled by Forced $\Phi^{6}$-Van der Pol Equation

The aim of this paper is to investigate global bifurcations and chaotic dynamics for the nonlinear model oscillations of a the cardiac pacemaker device subjected to a harmonic excitation by using a perturbation method based on the Melnikov theory. First,the model equation is derived and it is shown that it dynamics can be describe by a modified Van der Pol oscillator. Then, from Melnikov theory, we obtain the conditions for the existence of homoclinic and heteroclinic bifurcation in the case of the $\Phi^6$ potential is bounded. Finally,the results of numerical simulation are given and also show that the Melnikov chaotic motions threshold.