东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2005, Vol. 26 ›› Issue (10): 926-929.DOI: -

• 论著 • 上一篇    下一篇

一类种群增长模型的反馈线性化控制

张悦;张庆灵;赵立纯;刘佩勇   

  1. 东北大学理学院;东北大学理学院;鞍山师范学院数学系;东北大学理学院 辽宁沈阳110004
  • 收稿日期:2013-06-24 修回日期:2013-06-24 出版日期:2005-10-15 发布日期:2013-06-24
  • 通讯作者: Zhang, Y.
  • 作者简介:-
  • 基金资助:
    辽宁省普通高校学科带头人基金资助项目(124210)

Feedback-linearized control of a class of population growth models

Zhang, Yue (1); Zhang, Qing-Ling (1); Zhao, Li-Chun (2); Liu, Pei-Yong (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) Department of Mathematics, Anshan Normal College, Anshan 114005, China
  • Received:2013-06-24 Revised:2013-06-24 Online:2005-10-15 Published:2013-06-24
  • Contact: Zhang, Y.
  • About author:-
  • Supported by:
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摘要： 考虑一类带有时滞的种群增长模型的混沌控制问题.通过计算系统的Lyapunov指数和Lyapunov维数验证了一类带有时滞的种群增长模型具有混沌现象.运用反馈线性化方法,设计反馈控制器,对成虫进行捕获或投放,制定合理的开发策略,将系统中的混沌轨道稳定到理想的目标轨道,即不稳定的不动点,进而使不稳定的种群系统达到稳定.数值仿真说明该反馈控制器行之有效,可以使处于混沌状态的生物种群稳定到理想状态,实现种群的有序生存,保持自然界的生态平衡.

关键词: Lyapunov指数, Lyapunov维数, 混沌控制, 反馈线性化, 不动点

Abstract: Discusses the problem of the chaotic control of a class of population growth models with time lag. Computing the Lyapunov exponents and Lyapunov dimension of the system, the fact that there is a chaos phenomenon in the population growth models with time lag is verified. A feedback controller is designed to capture or release adult population by feedback linearization as to stabilize the chaotic orbits and enable them to be ideal target ones, i.e., unstable fixed points of the chaotic system. The unstable population system will therefore become stable by a rational development policy. Numerical simulations indicate that this feedback controller is effective in practice. It will cause the biological population in chaos states to stabilize and come into an ideal state, thus realizing orderly existence with balance of nature maintained for long.

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