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Stability and Neimark-Sacker bifurcation analysis of a food-limited population model with a time delay

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【作者】 姜晓伟； 关治洪； 张先鹤； 张顶学； 刘峰；

【Author】 Jiang Xiao-Wei a),Guan Zhi-Hong a),Zhang Xian-He b),Zhang Ding-Xue c),and Liu Feng d) a) Department of Control Science and Engineering,Huazhong University of Science and Technology,Wuhan 430074,China b) College of Mechatronics and Control Engineering,Hubei Normal University,Huangshi 435002,China c) Petroleum Engineering College,Yangtze University,Jingzhou 434023,China d) Department of Electronic Information and Mechanics,China University of Geosciences,Wuhan 430074,China

【机构】 Department of Control Science and Engineering,Huazhong University of Science and Technology； College of Mechatronics and Control Engineering,Hubei Normal University； Petroleum Engineering College,Yangtze University； Department of Electronic Information and Mechanics,China University of Geosciences；

【摘要】 In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.

【Abstract】 In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results.

【关键词】 food-limited model； time delay； Neimark-Sacker bifurcation； periodic solution；
【Key words】 food-limited model； time delay； Neimark-Sacker bifurcation； periodic solution；
【基金】 Project supported by the National Natural Science Foundation of China (Grant Nos. 61272069,61272114,61073026,61170031,and 61100076)
  • 【文献出处】 Chinese Physics B ,中国物理B , 编辑部邮箱 ,2013年03期
  • 【分类号】O242.2
  • 【被引频次】2
  • 【下载频次】69
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