Chaos synchronization of two stochastic Duffing oscillators by feedback control

This paper addresses chaos synchronization of two identical stochastic Duffing oscillators with bounded random parameters subject to harmonic excitations. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by Gegenbauer polynomial approximation, so that the chaos synchronization problem of stochastic Duffing oscillators can be reduced into that of the equivalent deterministic systems. Then a feedback control strategy is adopted to synchronize chaotic responses of two identical equivalent deterministic systems under different initial conditions. The feedback parameters are determined through analysis of the top Lyapunov exponent of the variational equation of the controlled responding system. Numerical analysis shows that the feedback control strategy is an effective way to synchronize two identical stochastic Duffing systems.