| 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.[点击复制] |
| ZHANG Qi-min, NIE Zan-kan.Exponential stability of stochastic age-dependent population dynamics system[J].Control Theory and Technology,2004,21(6):907~910.[点击复制] |
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| 一类随机人口发展系统的指数稳定性 |
| Exponential stability of stochastic age-dependent population dynamics system |
| 摘要点击 1868 全文点击 1610 |
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| DOI编号 10.7641/j.issn.1000-8152.2004.6.015 |
| 2004,21(6):907-910 |
| 中文关键词 随机系统 It^o公式 人口 指数稳定性 |
| 英文关键词 stochastic system It formula population exponential stability |
| 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 |
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| 中文摘要 |
| 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 |
| 英文摘要 |
| 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. |
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