Stochastic period-doubling bifurcation analysis of a Roessler system with a bounded random parameter

This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Roessler system with an arch-like bounded random parameter. First, we transform the stochastic Roessler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Roessler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Roessler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Roessler system. (general)