Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays | Zendy

Long Li | Zendy; Yanxia Zhang | Zendy

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Dynamic Analysis and Hopf Bifurcation of a Lengyel–Epstein System with Two Delays

Author(s) -

Long Li,

Yanxia Zhang

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/5554562

Subject(s) - mathematics , center manifold , hopf bifurcation , bifurcation diagram , saddle node bifurcation , stability (learning theory) , pitchfork bifurcation , biological applications of bifurcation theory , transcritical bifurcation , mathematical analysis , bifurcation , control theory (sociology) , nonlinear system , physics , control (management) , management , quantum mechanics , machine learning , computer science , economics

In this paper, a Lengyel–Epstein model with two delays is proposed and considered. By choosing the different delay as a parameter, the stability and Hopf bifurcation of the system under different situations are investigated in detail by using the linear stability method. Furthermore, the sufficient conditions for the stability of the equilibrium and the Hopf conditions are obtained. In addition, the explicit formula determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained with the normal form theory and the center manifold theorem to delay differential equations. Some numerical examples and simulation results are also conducted at the end of this paper to validate the developed theories.

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