Stability and Neimark-Sacker bifurcation analysis of food-limited population model with time delay |
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| Authors: | Jiang Xiao-Wei Guan Zhi-Hong Zhang Xian-He Zhang Ding-Xue Liu Feng |
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| Affiliation: | a Department of Control Sclience 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 |
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| Abstract: | In this paper, a kind of discrete delay food-limited model obtained by 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 some 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. |
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| Keywords: | food-limited model time delay Neimark-Sacker bifurcation periodic solution |
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