首页 | 本学科首页   官方微博 | 高级检索  
     

一类随机人口发展系统的指数稳定性
引用本文:张启敏,聂赞坎. 一类随机人口发展系统的指数稳定性[J]. 控制理论与应用, 2004, 21(6): 907-910
作者姓名:张启敏  聂赞坎
作者单位:宁夏大学,数学计算机学院,宁夏,银川,750021;西安交通大学,理学院,陕西,西安,710049
基金项目:宁夏自然科学基金项目 (G002); 宁夏高等学校科学研究项目
摘    要:对人口系统的讨论 ,通常的数学模型没有考虑外界环境对系统的影响 .在假设随机的外界环境对迁移产生扰动的条件下 ,给出Hilbert空间中一类随机时变人口发展系统 .对随机时变人口发展系统的均方稳定性和指数稳定性进行了讨论 .利用Burkholder_Davis_Gundy不等式 ,Gronwall引理和Kolmogorov不等式得到了均方稳定和指数稳定的充分条件 .最后提出如果生育率选作控制变量 ,系统仍然是均方和指数稳定的 ,并可进一步讨论它的最优控制问题

关 键 词:随机系统  It公式  人口  指数稳定性
文章编号:1000-8152(2004)06-0907-04

Exponential stability of stochastic age-dependent population dynamics system
ZHANG Qi-min,NIE Zan-kan. Exponential stability of stochastic age-dependent population dynamics system[J]. Control Theory & Applications, 2004, 21(6): 907-910
Authors:ZHANG Qi-min  NIE Zan-kan
Affiliation:School of Mathematics and Computer,Ningxia University,Yinchuan Ningxia 750021,China; School of Science,Xi'an Jiaotong University,Xi'an Shaanxi 710049,China
Abstract:The influence of the stochastic external environment upon the population dynamics system have never been considered in ordinary age-dependent system models.A class of stochastic age-dependent population dynamics system is proposed,on the condition that migration is perturbed by random external environment.The mean square and almost sure exponential stability of stochastic age-dependent population dynamics system are discussed in Hilbert space.Sufficient conditions of mean square and almost sure exponential stability are established for a class of stochastic age-dependent population dynamics system.The analyses are conducted by using Burkholder-Davis-Gundy inequality,Gronwall lemma and Kolmogorov inequality derived for our stability purposes.It is also proposed that if the birth rate can be regarded as a controllable variable,the system is still mean square and almost sure exponential stability.The optimal control can be further studied for stochastic age-dependent population dynamics system.
Keywords:stochastic system   It formula   population   exponential stability
本文献已被 CNKI 维普 万方数据 等数据库收录!
点击此处可从《控制理论与应用》浏览原始摘要信息
点击此处可从《控制理论与应用》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号