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

Author

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  • Daiyong Wu
  • Hai Zhang
  • Jinde Cao
  • Tasawar Hayat

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.

Suggested Citation

  • Daiyong Wu & Hai Zhang & Jinde Cao & Tasawar Hayat, 2013. "Stability and Bifurcation Analysis of a Nonlinear Discrete Logistic Model with Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, December.
    • Handle: RePEc:hin:jnddns:463059
    DOI: 10.1155/2013/463059
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