[1]赵朝锋,张启敏.带Markov跳随机种群收获系统数值解的指数稳定性[J].华侨大学学报(自然科学版),2012,33(4):472-476.[doi:10.11830/ISSN.1000-5013.2012.04.0472]
　ZHAO Chao-feng,ZHANG Qi-min.Exponential Stability of Numerical Solutions to Nonlinear Stochastic Harvesting Population System with Markov Jumps[J].Journal of Huaqiao University(Natural Science),2012,33(4):472-476.[doi:10.11830/ISSN.1000-5013.2012.04.0472]
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带Markov跳随机种群收获系统数值解的指数稳定性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第4期
页码:
472-476
栏目:
出版日期:
2012-07-20

文章信息/Info

Title:
Exponential Stability of Numerical Solutions to Nonlinear Stochastic Harvesting Population System with Markov Jumps
文章编号:
1000-5013(2012)04-0472-05
作者:
赵朝锋1;  张启敏1; 2
1. 北方民族大学 信息与计算科学学院, 宁夏 银川 750021;2. 宁夏大学 数学计算机学院, 宁夏 银川 750021
Author(s):
ZHAO Chao-feng1;  ZHANG Qi-min1; 2
1. School of Informatics and Computer Science, Beifang University of Nationalities, Yinchuan 750021, China; 2. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China
关键词:
Markov跳;  随机种群模型;  Ito公式;  数值解;  稳定性
Keywords:
Markov jump;  stochastic population model;  Ito formula;  numerical solution;  stability
分类号:
O175.21
DOI:
10.11830/ISSN.1000-5013.2012.04.0472
文献标志码:
A
摘要:
研究一类带跳的非线性随机种群收获动力学模型的数值解指数稳定性的问题,给出了外界环境对系统产生影响的条件下带跳的随机收获动力学系统.通过一些特殊不等式, Ito公式及Burkholder-Davis-Gundy不等式,讨论了带Markov随机种群系统数值解的收敛性,得到了数值解指数稳定所满足的充分条件,所得结论是确定性种群系统的扩展.
Abstract:
A harvesting exponential stability of numerical solution for nonlinear stochastic population system with jump is studied with the external environment impact on the system of Markov jump. One sufficient condition for the exponential stability of numerical solution is obtained through some special inequality, Ito formula and Burkholder-Davis-Gundy inequality. The obtained result is the expansion of certainty population system.

参考文献/References:

[1] ARNOLD L.Stochastic differential equations: Theory and applications[M].Detroit: Wiley,1972.
[2] ZHANG Qi-min,HAN Chang-zhao.Numerical analysis for stochastic age-structured population equations[J].Applied Mathmatics and Computation,2005,169(1):278-294.
[3] LI Rong-hua,MENG Hong-bing,CHANG Qin.Convergence of numerical solutions to stochastic age-dependent population equations[J].Comput Appl Math,2006,193(1):109-120.
[4] ZHANG Qi-min,LIU Wen-an,NIE Zan-kan.Existence, uniqueness and exponential stability for stochastic age-dependent population[J].Appl Math Comput,2004,154(1):183-201.
[5] 李鸿.一种单种群收获模型的稳定性分析[J].生物数学学报,2001,16(1):63-69.
[6] PANG Wan-kai,LI Rong-hua, LIU Ming.Exponential stability of numerical solutions to stochastic age-dependent population equations[J].Applied Mathematics and Computation,2006,183(1):152-159.
[7] ZHOU Shao-bo,WU Fu-ke.Convergence of numerical solution to neutral stochastic delay differential equation with Markovian switching[J].Journal of Computational and Applied Mathematics,2009,229(1):85-96.
[8] 何荣泽,王绵森.一类非线性周期种群系统的最优收获控制[J].应用数学,2003,16(3):88-93.

备注/Memo

备注/Memo:
收稿日期: 2011-12-23
通信作者: 张启敏(1964-),女,教授,主要从事控制理论和及其应用的研究.E-mail:zhangqimin64@sina.com.
基金项目: 国家自然科学基金资助项目(11061024)
更新日期/Last Update: 2012-07-20