Nonlinear Dynamics and Active Control in a Liénard-Type Oscillator under Parametric and External Periodic Excitations

In this paper, nonlinear dynamics and active control of a Lienard-type oscillator under parametric and external excitations are investigated. The amplitude of the harmonic oscillations and the criteria for the appearance of the Melnikov chaos are derived and analyzed. Analytical predictions are demonstrated through direct numerical simulation. Various bifurcations structures of the system with a single well potential and a double well potential are analyzed. The effects of the control gain parameter on the dynamical behaviour of the forced Lienard-type oscillator are analyzed. As results, it is found that for an appropriate value of the control gain parameter, the chaotic behaviour is completely removed of the system.