色噪声激励下含分数阶时滞项的广义Van der Pol系统的随机分岔  

Stochastic bifurcation of generalized Van der Pol systems with fractional order delay under colored noise excitation

作　　者：王媛 王慧男 盛正大 王芳 WANG Yuan;WANG Huinan;SHENG Zhengda;WANG Fang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou,Gansu 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《内江师范学院学报》2023年第12期48-54,共7页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(61863022)。

摘　　要：研究了在色噪声激励下含分数阶时滞项的广义Van der Pol系统的随机分岔问题.首先将其中的分数阶导数项转换为一种回复力和阻尼力的线性组合,利用均方误差最小原则,通过计算与原系统的误差,可将原分数阶系统转换为整数阶系统.其次引入广义Van der Pol变换,根据随机平均法求得系统的伊藤随机微分方程和Fokker-Planck-Kolmogorov(FPK)方程.最后通过系统的稳态概率密度函数图验证了分数阶导数阶数p、非线性阻尼系数μ等参数的改变可以诱发系统的随机P-分岔.The stochastic bifurcation problem of a generalized Van der Pol system with fractional order delay excited by colored noise is studied.Firstly,the fractional derivative term is transformed into a linear combination of restoring force and damping force,using the principle of minimum mean square error,by calculating the error with the original system,the original fractional order system can be transformed into integer order system.Secondly,the generalized Van der Pol transformation is introduced,based on the stochastic averaging method for system of It stochastic differential equations and Fokker-Planck-Kolmogorov(FPK)equations.Finally,through the steady-state probability density function diagram of the system,it is verified that the change of fractional derivative order p and nonlinear damping coefficient μ can induce stochastic P-bifurcation of the system.

关 键 词：色噪声 分数阶 广义Van der Pol系统 时滞反馈 随机P-分岔 

分 类 号：O324[理学—一般力学与力学基础]