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 。
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.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2004年第6期907-910,共4页
Control Theory & Applications
基金
宁夏自然科学基金项目 (G0 0 2 )
宁夏高等学校科学研究项目
关键词
随机系统
Ito^公式
人口
指数稳定性
stochastic system
It formula
population
exponential stability
