Dichotomous-noise-induced chaos in a generalized Duffing-type oscillator with fractional-order deflection

The chaotic behavior of a generalized Duffing-type oscillator with fractional-order deflection under dichotomous noise excitation is discussed in detail. Using the Melnikov method together with mean-square criterion, necessary conditions for the onsets of chaos are derived. It is shown that with the increase of noise transition rate, the threshold of noise amplitude for chaos firstly decreases to a minimum, and then increases. The effects of dichotomous noise on the Duffing-type oscillator are also obtained by vanishing the mean largest Lyapunov exponent of the oscillator. This is further verified by phase portraits and time histories with numerical simulations.