Abstract
Duffing–Van der Pol equation with the fifth nonlinear-restoring force is investigated. The bifurcation structure and chaotic motion under the periodic perturbation are obtained by numerical simulations. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, phase portraits and Poincaré maps, exhibit some new complex dynamical behaviors of the system. Different routes to chaos, such as period doubling and quasi-periodic routes, and various kinds of strange attractors are also demonstrated.
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