Effect of nonlinear dissipation on the basin boundaries of a driven two-well Modified Rayleigh-Duffing Oscillator

Abstract

This paper considers effect of nonlinear dissipation on the basin boundaries of a driven two-well Modified Rayleigh-Duffing Oscillator where pure and unpure quadratic and cubic nonlinearities are considered. By analyzing the potential, an analytic expression is found for the homoclinic orbit. The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of our oscillator. It is found the effects of unpure quadratic parameter and amplitude of parametric excitation on the critical Melnikov amplitude $\mu_{cr}$. Finally, we examine carefully the phase space of initial conditions in order to analyze the effect of the nonlinear damping, and particular how the basin boundaries become fractalized.