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Stochastic Chaos and its control in a stochastic Duffing-van der Pol system

The stochastic Double-Well Duffing-van der Pol (SDVP for short) system with bounded random parameter is first transformed into an equivalent deterministic system by the Chebyshev polynomial approximation method, and then the stochastic chaos and its control by noise are investigated. Therefore the problem of controlling stochastic chaos in the SDVP system can be reduced into the problem of controlling deterministic chaos in the equivalent system. The numerical simulations show that the chaos behavior in the SDVP system is by and large similar to that in the equivalent deterministic Duffing-Van der Pol (DVP for short) system. The chaos behavior can be controlled to the period states by noise, and with the effect of the random parameter and its intensity, there are still some features.
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