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

doi:10.1088/1674-1056/22/3/030204

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.

Keywords: food-limited model time delay Neimark-Sacker bifurcation periodic solution

Received: 11 June 2012
Revised: 15 August 2012
Accepted manuscript online:

PACS:	02.30.Ks	(Delay and functional equations)
	02.30.Oz	(Bifurcation theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 60973012, 61073025, 61073026, 61170031, and 61100076).

Corresponding Authors: Guan Zhi-Hong
E-mail: zhguan@mail.hust.edu.cn

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Jiang Xiao-Wei (姜晓伟), Guan Zhi-Hong (关治洪), Zhang Xian-He (张先鹤), Zhang Ding-Xue (张顶学), Liu Feng (刘峰) Stability and Neimark-Sacker bifurcation analysis of food-limited population model with time delay 2013 Chin. Phys. B 22 030204

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

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