一类分数阶随机双稳系统的稳态概率密度计算与分析  

Analysis and calculation of steady-state probability density in a fractional-order bistable system driven by Lévy noise

作　　者：陈昊宇 郭永峰 余勤[1] CHEN Haoyu;GUO Yongfeng;YU Qin(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《华中师范大学学报(自然科学版)》2025年第2期197-202,共6页Journal of Central China Normal University:Natural Sciences

基　　金：国家自然科学基金项目(11672207);天津市自然科学基金项目(17JCYBJC15700).

摘　　要：分数阶双稳系统具有全局相关性和非局部特性,已被成功地应用于许多实际问题模型的构建.该文用最小均方误差准则推导出等效的分数阶双稳系统,并通过四阶Runge-Kutta算法数值模拟系统的稳态概率密度,进而对分数阶双稳系统在乘性高斯白噪声和加性Lévy噪声共同作用下的相变行为进行分析.研究发现,Lévy噪声强度、稳定性指标、偏斜参数和分数阶阶数可诱导系统产生相变现象,且高斯噪声强度的增加使得稳态概率密度整体峰值减小,而分数阶阶数的增加使得稳态概率密度左侧峰值增加明显.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.

关 键 词：分数阶双稳系统 高斯白噪声 Lévy噪声 稳态概率密度 相变行为 

分 类 号：O211[理学—概率论与数理统计]