Effect of nonlinear dissipation on the basin boundaries of a driven two-well Rayleigh–Duffing oscillator

The Rayleigh oscillator is one canonical example of self-excited systems. However, simple generalizations of such systems, such as the Rayleigh–Duffing oscillator, have not received much attention. The presence of a cubic term makes the Rayleigh–Duffing oscillator a more complex and interesting case to analyze. In this work, we use analytical techniques such as the Melnikov theory, to obtain the threshold condition for the occurrence of Smale-horseshoe type chaos in the Rayleigh–Duffing oscillator. Moreover, we examine carefully the phase space of initial conditions in order to analyze the effect of the nonlinear damping, and in particular how the basin boundaries become fractalized.