  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.
