Resonance and Chaos Analysis of a Hybrid Rayleigh-Van Der Pol-Duffing System With Two Harmonic Excitations

Abstract In this paper, the dynamical properties of a hybrid Rayleigh-van der Pol-Duffing system subjected to two external periodic excitations are investigated, focusing on primary resonance, primary-superharmonic combined resonance, and primary-subharmonic resonance, as well as the chaotic dynamic. The method of multiple scales is employed to derive the first-order approximate analytical solution of system. The stability conditions for steady-state periodic solutions are obtained, and the influence of system parameters on the amplitude and stability of steady-state periodic solutions is analyzed through the frequency–amplitude equations. Furthermore, the Melnikov method is applied to conduct a global analysis of the system and yield the threshold of chaos in different cases of harmonic excitation frequencies. Numerical simulations of the system are conducted to obtain frequency–amplitude curves, time histories, phase trajectories, and maximum Lyapunov exponent, thereby analyzing the influence of parameters on the system's dynamic characteristics and verifying the theoretical analysis results.