Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation

Abstract EN

Fractional-order calculus is more competent than integer-order one when modeling systems with properties of nonlocality and memory effect.

And many real world problems related to uncertainties can be modeled with stochastic fractional-order systems with random parameters.

Therefore, it is necessary to analyze the dynamical behaviors in those systems concerning both memory and uncertainties.

The period-doubling bifurcation of stochastic fractional-order Duffing (SFOD for short) system with a bounded random parameter subject to harmonic excitation is studied in this paper.

Firstly, Chebyshev polynomial approximation in conjunction with the predictor-corrector approach is used to numerically solve the SFOD system that can be reduced to the equivalent deterministic system.

Then, the global and local analysis of period-doubling bifurcation are presented, respectively.

It is shown that both the fractional-order and the intensity of the random parameter can be taken as bifurcation parameters, which are peculiar to the stochastic fractional-order system, comparing with the stochastic integer-order system or the deterministic fractional-order system.

Moreover, the Chebyshev polynomial approximation is proved to be an effective approach for studying the period-doubling bifurcation of the SFOD system.