Abstract：With global dependence and non-local properties， the fractional-order system has been successfully applied to the construction of many practical models. Thus， it is very important to study the phase transition behavior of the fractional-order bistable system. In this paper， an equivalent fractional-order bistable system is derived by using the minimum mean square error rule， then we conducts numerical simulations through the fourth-order Runge-Kutta algorithm， and analyzes the phase transition behavior of the fractional-order bistable system under multiplicative Gaussian white noise and additive Lévy noise. It is found that the Lévy noise intensity， stability index， skew parameter and fractional order can induce the phase transition， and the increase of Gaussian noise intensity decreases the whole peak value of steady-state probability density， the increase of the fractional order makes the peak value on the left side of the steady-state probability density increase significantly.
陈昊宇,郭永峰,余 勤. 一类分数阶随机双稳系统的稳态概率密度计算与分析[J]. 华中师范大学学报(自然科学版), 2025, 59(2): 197-202.
CHEN Haoyu,GUO Yongfeng,YU Qin. Analysis and calculation of steady-state probability density in a fractional-order bistable system driven by Lévy noise. journal1, 2025, 59(2): 197-202.
2025, Vol. 59 
