Stability and Bifurcation Analysis of a Nonlinear Discrete Logistic Model with Delay

Daiyong Wu, Hai Zhang, Jinde Cao and Tasawar Hayat

Discrete Dynamics in Nature and Society, 2013, vol. 2013, 1-7

Abstract:

We consider a nonlinear discrete logistic model with delay. The characteristic equation of the linearized system at the positive equilibrium is a polynomial equation involving high order terms. We obtain the conditions ensuring the asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcation, with respect to the parameter of the model. Based on the bifurcation theory, we discuss Neimark-Sacker bifurcation direction and the stability of bifurcated solutions. Finally, some numerical simulations are performed to illustrate the theoretical results.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:463059

DOI: 10.1155/2013/463059

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