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Stability and Neimark-Sacker bifurcation analysis of a food-limited population model with a time delay 被引量:2

Stability and Neimark-Sacker bifurcation analysis of a food-limited population model with a time delay
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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. 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.
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第3期67-71,共5页 中国物理B(英文版)
基金 Project supported by the National Natural Science Foundation of China (Grant Nos. 61272069,61272114,61073026,61170031,and 61100076)
关键词 food-limited model time delay Neimark-Sacker bifurcation periodic solution food-limited model,time delay,Neimark-Sacker bifurcation,periodic solution
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