Stochastic chaos and its control in the stochastic Bonhoeffer-Van der Pol system

Abstract

In this paper, the stochastic chaos of the stochastic Bonhoeffer-Van der Pol system with bounded random parameter and its control by noise are investigated. The stochastic Bonhoeffer-Van der Pol system is first transformed into an equivalent deterministic system using the Chebyshev polynomial approximation, so that the problem of controlling stochastic chaos is reduced to the problem of controlling deterministic chaos in the equivalent system. Thus, the top Lyapunov exponent of the equivalent system can be used to examine the chaotic behavior and its control of the responses. The numerical simulations show that the chaos behavior in the stochastic Bonhoeffer-Van der Pol system is by and large similar to that in the equivalent deterministic Bonhoeffer-Van der Pol system. The chaos behavior can be controlled to the periodic states by noise, but under the effect of the random parameter and its intensity, it has cortain specific features.