Strange attractors in a parametrically excited nonlinear oscillator

Abstract

Nonlinear oscillators exhibit rich and complex dynamic behaviour and are highly sensitive to initial conditions. The current paper studies the existence of strange attractors in a nonlinear oscillator namely the Duffing oscillator under harmonically varying parametric excitation. Numerical simulation is carried out via fourth-order Runge-kutta algorithm to study the presence of strange attractors in a parametrically excited nonlinear oscillator for different values of control parameters viz. coefficient of damping, frequency and amplitude of parametric excitation. For amplitude of parametric excitation d = 6.25 and frequency of parametric excitation Ω = 0.5, with coefficient of damping c = 0.2, the phase plane trajectory and time history show existence of classical chaotic attractors. There is oscillation between two chaotic attractors in a double well potential for every period of excitation. For amplitude of parametric excitation d = 6.25 and frequency of parametric excitation Ω = 0.07, with coefficient of damping c = 0.2, the system also shows the presence of two co-existing fixed point chaotic attractors which is found to merge with change in the parameter values. The dynamical behaviour of the fixed point chaotic attractors are found to be different from that of classical chaotic attractors.