色噪声与乘性信号驱动下昆虫爆发系统的稳定性和随机共振  

The Steady State Property and Stochastic Resonance for an Insect Outbreak Model Driven by Colored Noises and a Multiplicative Periodic Signal

作　　者：方次军[1,2] 刘先斌[1] FANG Cijun;LIU Xianbin(State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 210016, China;School of Science, Hubei University of Technology, Wuhan Hubei 430068, China)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,江苏南京210016 [2]湖北工业大学理学院,湖北武汉430068

出　　处：《江西师范大学学报（自然科学版）》2017年第6期623-628,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10672074;11072107)资助项目

摘　　要：研究的是一类受色噪声和乘性周期信号驱动的昆虫爆发系统的稳定性和随机共振现象.首先对于一类由色交叉关联噪声驱动的昆虫爆发种群系统,通过应用FPK方程,获取了系统的稳态概率分布函数的近似表达式,重点讨论了噪声强度及自相关时间对此类昆虫爆发系统稳定性的影响;然后通过加入弱乘性周期信号,根据快速下降法和两态理论给出了信噪比公式,研究了噪声及其关联时间对于昆虫系统信噪比的影响.进而分析它们对系统种群数的稳定性和延续存活时间的一些实际作用.The steady state behavior and the stochastic resonance of an insect outbreak model induced by colored noises and a multiplicative periodic signal are studied.Firstly,for an insect outbreak model driven by colored correlation of noises.The steady state probability distribution function of the system is obtained by applying the Fokker-Planck equation.The influence of noises intensity and correlation time on the stability of the system are discussed.Then by adding the weak multiplicative periodic signal,the signal noise ratio formula is given by the fast descent method and the two-state theory.The influence of noises intensity and correlation time on the SNR of the insect system are studied.Consequently,the stability of the system population and the actual survival time are analyzed.

关 键 词：昆虫爆发模型 色噪声 FPK方程 稳态概率分布函数 随机共振 

分 类 号：O324[理学—一般力学与力学基础]