具有扩散项和Lévy噪声的随机年龄结构种群系统的指数稳定性  

Exponential stability of stochastic age-structured population system with diffusion and Lévy noise

作　　者：韩婷[1] 李国平[1] 马维军 HAN Ting;LI Guo-ping;MA Wei-jun(Xinhua College of Ningxia University,Yinchuan Ningxia 750021,China;School of Information Engineering,Ningxia University,Yinchuan Ningxia 750021,China)

机构地区：[1]宁夏大学新华学院,宁夏银川750021 [2]宁夏大学信息工程学院,宁夏银川750021

出　　处：《控制理论与应用》2023年第8期1449-1456,共8页Control Theory & Applications

基　　金：宁夏自然科学基金项目(2022AAC03642,2023AAC03017);国家自然科学基金项目(62063028);宁夏高等学校科学研究项目(NGY2022114)资助。

摘　　要：稳定性是种群生物学和控制论研究的重要内容之一.现实世界中,外界随机因素对种群稳定性的影响较大.本文讨论了具有扩散项和Lévy噪声的随机年龄结构种群系统的指数稳定性,通过运用随机分析理论、BurkholderDavis-Gundy不等式、Chebyshev不等式等工具对系统随机能量等式中的系数函数进行估计,得到了新的指数稳定性和几乎必然指数稳定性的充分条件.最后,本文给出例子并对其进行数值模拟,验证了理论的有效性.Stability is one of the most important topics in population biology and control.In the real world,external random factors have a great influence on the stability of population.In this paper,we focus on the exponential stability for a stochastic age-structured population system with diffusion and Lévy noise.With the help of the stochastic analysis´theory,the Burkholder-Davis-Gundy inequality,and the Chebyshev inequality et al.,the coefficients functions in the stochastic energy equality of the system are estimated.Some novel sufficient conditions on exponential stability and almost sure exponential stability are established.Finally,an example and its numerical simulation are given to illustrate the effectiveness of the theoretical results.

关 键 词：随机种群系统 扩散 噪声 能量等式 稳定性 

分 类 号：Q141[生物学—生态学] O211.6[生物学—普通生物学]