Effect of amplitude modulated signal on chaotic motions in a mixed Rayleigh–Liénard oscillator

Abstract

This paper addresses the issues of the control of chaotic motions in a mixed Rayleigh-Liénard oscillator by amplitude modulated excitation. The Melnikov method is used to analytically determine the domains boundaries where horseshoes chaos appears. The basin of attraction has been drawn to confirm the horseshoes chaos appearance domain. Routes to chaos are investigated through bifurcations structures, Lyapunov exponent, phase portraits and Poincaré section. The effects of control force on chaotic motions are strongly analyzed and the control efficiency is found where the cases of g = 0 (unmodulated case), g $\not equal$ 0 with $\Omega$ = ω and \frac{\Omega}{ω} $\not equal$ \frac{q }{p} where p and q are simple positive integers are considered. Results of analytical investigations are validated and complemented by numerical simulations.