The twofold influence of non-periodic force on chaos control

The influences of a kind of non-periodic force, modeled by bounded noise or chaotic driving, on chaos control of nonlinear dynamical system are studied. Suppressing chaos as well as inducing chaos in a periodically driven Duffing-van der Pol oscillator with 5 nonlinear components is studied in detail. By examining the separation distance, the largest Lyapunov exponent, the scaling exponent of power spectrum, and the Poincaré map of the considered oscillator, it is found that the non-periodic driving of appropriate amplitude, on one hand, can eliminate the sensitive dependence on initial conditions, then suppress the chaotic behavior and convert a chaotic attractor to a strange but nonchaotic one in this DVP oscillator. On the other hand, it can induce the chaotic behavior and then convert a periodic attractor to a chaotic one as well. Thus, the dual roles of non-periodic driving, i.e. suppressing and inducing chaos, in chaos control of nonlinear dynamical systems are revealed.