On the occurrence of chaos in a parametrically driven extended Rayleigh oscillator with three-well potential

We examine the chaotic behavior of an extended Rayleigh oscillator in a three-well potential under additive parametric and external periodic forcing for a specific parameter choice. By applying Melnikov method, we obtain the condition for the existence of homoclinic and heteroclinic chaos. The numerical solution of the system using a fourth-order Runge-Kutta method confirms the analytical predictions and shows that the transition from regular to chaotic motion is often associated with increasing the energy of an oscillator. An analysis of the basins of attraction showing fractal patterns is also carried out.