Onset of colored-noise-induced chaos in the generalized Duffing system

The effects of colored noise, red noise and green noise, on the onset of chaos are investigated theoretically and confirmed numerically in the generalized Duffing system with a fractional-order deflection. Analytical predictions concerning the chaotic thresholds in the parameter space are derived by using the stochastic Melnikov method combined with the mean-square criterion. To qualitatively confirm the analytical results, numerical simulations obtained from the mean largest Lyapunov exponent are used as test beds. We show that colored noise can induce chaos, and the effects for the case of red noise on the onset of chaos differ from those for the case of green noise. The most noteworthy result of this work is the formula, which relates the chaotic thresholds among red, green and white noise, holds for noise-induced chaos in the Duffing system. We also show that Gaussian white noise can induce chaos more easily than colored noise.