Abstract and Applied Analysis

Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function

Chongwu Zheng, Fengqin Zhang, and Jianquan Li

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A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 136707, 8 pages.

First available in Project Euclid: 2 October 2014

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Zheng, Chongwu; Zhang, Fengqin; Li, Jianquan. Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function. Abstr. Appl. Anal. 2014 (2014), Article ID 136707, 8 pages. doi:10.1155/2014/136707. https://projecteuclid.org/euclid.aaa/1412276917

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