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

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 o...

Full description

Saved in:
Bibliographic Details
Main Authors: Daiyong Wu, Hai Zhang, Jinde Cao, Tasawar Hayat
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2013/463059
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1026-0226
1607-887X