Regular and Chaotic Behaviors of Modified Rayleigh-Duffing oscillator

The regular and chaotic behavior of modified Rayleigh-Duffing oscilla-tor is studied. We consider in this paper the dynamics of Modified Rayleigh–Duffing oscillator. The harmonic balance method are used to find the amplitudes of the oscillatory states, and analyze. The in-fluence of system parameters are clearly found on the bifurcations in the response of this system is investigated. It is found also hysteresis and jump phenomenon are appered or desappered when certain parameters incrases or descrases. Various bifurcation structures, the variation of the Lyapunov ex-ponent are obtained, using numerical simulations of the equations of motion. Various basin attraction are used to confirm the predictions of bifurcation structures and its corresponds Lyapunov exponent.