Hopf-zero bifurcation of Oregonator oscillator with delay

Advances in Difference Equations

Yuting Cai¹  Liqin Liu¹  Chunrui Zhang¹ 

[1] Department of Mathematics, Northeast Forestry University;

关键词: Oregonator model;    Delay;    Hopf-zero bifurcation;    Normal form;   

DOI  :  10.1186/s13662-018-1894-2

来源: DOAJ

【 摘 要 】

Abstract In this paper, we study the Hopf-zero bifurcation of Oregonator oscillator with delay. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, we get the normal form by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, we obtain a critical value to predict the bifurcation diagrams and phase portraits. Under some conditions, saddle-node bifurcation and pitchfork bifurcation occur along M and N, respectively; Hopf bifurcation and heteroclinic bifurcation occur along H and S, respectively. Finally, we use numerical simulations to support theoretical analysis.

【 授权许可】

Unknown