Dynamics of a stochastic system driven by cross-correlated sine-Wiener bounded noises

The sine-Wiener noise, as one new type of bounded noise and a natural tool to model fluctuations in dynamical systems, has been applied to problems in a variety of areas, especially in biomolecular networks and neural models. In this paper, by virtue of the Novikov theorem, Fox's approach, and the ansatz of Hanggi, an approximate Fokker-Planck equation is derived for an one-dimensional Langevin-type equation with cross-correlated sine-Wiener noise. Meanwhile, the dynamical characters of a bistable system driven by cross-correlated sine-Wiener noise are investigated by applying the approximate theoretical method. For the bistable system, the cross-correlation intensity can induce the reentrance-like phase transition, while the other noise intensities and the self-correlation time, except for the self-correlation time of additive bounded noise, can induce the first-order-like phase transition. The transition from the stable state to another one can be accelerated by (additive bounded noise intensity), 1 (the self-correlation time of the multiplicative bounded noise), and 2 (the self-correlation time of the additive bounded noise) and can be restrained with and 3 (self-correlation time of the cross-correlation bounded noise). It is interesting that the noise-enhanced stability phenomenon is observed with D (multiplicative bounded noise intensity) varying for the positive correlation (>0) and is enhanced as increases. The numerical results are in basic agreement with the theoretical predictions.