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2014 Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function
Chongwu Zheng, Fengqin Zhang, Jianquan Li
Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/136707

Abstract

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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Chongwu Zheng. Fengqin Zhang. Jianquan Li. "Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/136707

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021782
MathSciNet: MR3198146
Digital Object Identifier: 10.1155/2014/136707

Rights: Copyright © 2014 Hindawi

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