东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2014, Vol. 35 ›› Issue (5): 635-639.DOI: 10.12068/j.issn.1005-3026.2014.05.007

• 信息与控制 • 上一篇    下一篇

具有时滞的微分-代数生物模型的分岔与控制

张雪   

  1. (东北大学 理学院， 辽宁 沈阳110819)
  • 收稿日期:2013-07-25 修回日期:2013-07-25 出版日期:2014-05-15 发布日期:2014-08-18
  • 通讯作者: 张雪
  • 作者简介:张雪(1980-)，女，辽宁沈阳人，东北大学讲师，博士.
  • 基金资助:
    国家自然科学基金资助项目(61273008);辽宁省博士启动基金资助项目(20131026);中央高校基本科研业务费专项资金资助项目(N120405009).

Bifurcation and Control of DifferentialAlgebraic Biological Model with Time Delay

ZHANG Xue   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2013-07-25 Revised:2013-07-25 Online:2014-05-15 Published:2014-08-18
  • Contact: ZHANG Xue
  • About author:-
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摘要： 基于公共渔业经济理论，研究了一类带有时滞的食饵-捕食模型.研究表明:不考虑时滞的条件下，模型出现跨临界分岔，奇异诱导分岔，以及鞍结分岔现象，无捕获下，食饵种群与捕食者种群将共存且模型全局渐近稳定.在时滞存在的条件下，模型存在两个正平衡点，模型出现Hopf分岔现象和周期解，而且随着时滞的增加，模型平衡点的稳定性会随之发生变化.设计的状态反馈控制器可以有效消除模型的分岔，控制种群的变化.利用Matlab软件，数值仿真结果验证了结论的正确性.

关键词: 微分-代数生物模型, 跨临界分岔, 奇异诱导分岔, 鞍结分岔, Hopf分岔

Abstract: Considering the economic theory of public fishery， a preypredator bioeconomic model with time delay was studied. It was showed that transcritical bifurcation， singular induced bifurcation and saddlenode bifurcation would occur with no time delay. Under the condition of zero harvesting， prey and predator would be coexisted. With time delay， there existed two positive equilibrium points. Hopf bifurcation and small amplitude periodic solutions would occur， which caused switching of stability. The state feedback controller eliminated bifurcation phenomenon. By using Matlab software， the effectiveness of mathematical conclusions were verified by some numerical simulations.

Key words: differentialalgebraic bioeconomic model, transcritical bifurcation, singular induced bifurcation, saddlenode bifurcation, Hopf bifurcation

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