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

Daiyong Wu | Zendy; Hai Zhang | Zendy; Jinde Cao | Zendy; Tasawar Hayat | Zendy

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

Author(s) -

Daiyong Wu,

Hai Zhang,

Jinde Cao,

Tasawar Hayat

Publication year - 2013

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2013/463059

Subject(s) - bifurcation , mathematics , transcritical bifurcation , nonlinear system , stability (learning theory) , logistic function , bifurcation diagram , bifurcation theory , polynomial , mathematical analysis , control theory (sociology) , computer science , statistics , physics , control (management) , quantum mechanics , machine learning , artificial intelligence

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. Weobtain 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

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