Complex Dynamics in a Duffing–Van der Pol Oscillator with φ⁶ Potential

Abstract

The dynamical behavior of the extended Duffing–Van der Pol oscillator is investigated numerically in some detail. Different routes to chaos such as period-doubling bifurcation and intermittency, as well as various shapes of strange attractors and rich dynamical phenomena: crisis, transient chaos, are all observed by using bifurcation diagrams, phase projections and Poincaré maps. To characterize chaotic behavior of this oscillator system, the spectrum of Lyapunov exponent and Lyapunov dimension of the strange attractor are also employed.