双态噪声驱动的分数阶星型耦合网络的随机共振  

Stochastic resonance of fractional star-coupled network induced by dichotomous noise

作　　者：钟苏川 高仕龙[2] 史思红[3] 张路[4] ZHONG Su-Chuan;GAO Shi-Long;SHI Si-Hong;ZHANG Lu(College of Aeronautics and Astronautics,Sichuan University,Chengdu 610064,China;College of Mathematics and Physics,Leshan Normal University,Leshan 614000,China;College of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China;College of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学空天科学与工程学院,成都610064 [2]乐山师范学院数理学院,乐山614000 [3]海南师范大学数学与统计学院,海口571158 [4]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2024年第3期49-61,共13页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省自然科学基金(2022NSFSC1952);海南省自然科学基金(120QN250)。

摘　　要：本文研究了一类分数阶星型耦合网络模型的随机共振行为,该网络由一个中心粒子和多个耦合粒子组成,其中粒子的耦合强度受到双态噪声的扰动.本文将耦合粒子运动轨迹的算术平均值定义为系统的平均场,然后分别讨论了中心粒子和平均场的统计特征和共振行为.利用随机平均法及变换技巧,本文首先推导了中心粒子和平均场的一阶稳态矩和稳态响应振幅的表达式,然后分析了中心粒子和平均场的运动轨迹的一致性条件以及耦合粒子的同步条件,最后数值研究了中心粒子和平均场的共振行为.仿真结果显示,网络存在丰富的共振行为:中心粒子和平均场的稳态响应均可能出现“单峰共振”“单峰-单谷共振”“单谷-单峰共振”及“逆共振”等共振行为,说明中心粒子和平均场的稳态响应对参数的依赖性很高.此外,本文还基于中心粒子和平均场的稳态响应振幅给出了模型的共振区.本研究可望为分数阶星型网络共振行为的控制提供理论基础.In this paper,we investigate the stochastic resonance of a fractional star-coupled network model constructed by a central particle and multiple auxiliary particles,where the central particle is linked to each auxiliary particle with a coupled force fluctuated by dichotomous noise.We define the mean-field of the coupled particles as the average of trajectories of all auxiliary particles and discuss the statistical characteristic and resonance behavior of the central particle and the mean-field.By using the stochastic averaging method and some transformation techniques,we firstly obtain the analytic expressions for the first moment and amplitude of the central particle and mean-field.Then we analyze consistency condition of the trajectories of the central particle and mean-field as well as synchronization condition of the auxiliary particles.Finally,based on the expressions of steady-state response amplitude of the central particle and mean-field,resonance behavior ofthe network is numerically studied.It is shown that abundant resonance behaviors,such as“single-peak SR”,“single-peak and single-valley SR”,“single-valley and single-peak SR”and“inverse SR”can exhibit for both the central particle and the mean-field,which indicates that the resonance behavior of network are highly dependent on the system parameters.Additionally,resonance region of the network is given based on the expressions of steady-state response amplitude of the central particle and mean-field.It is expected that the obtained results can pave a way to the control of stochastic resonance of fractional star-coupled networks.

关 键 词：星型耦合网络 随机共振 双态噪声 分数阶Langevin系统 

分 类 号：O29[理学—应用数学]