Dynamic Properties Of The Coupled Oregonator Model With Delay

The coupling Oregonator is a typical coupled nonlinear system. In coupled oscillators with the delay, the delay will make dynamics change, while the effects by nature of oscillator itself and coupling strength can not be ignored. So it has important theoretical and practical significance to study coupled dynamic system.The main theoretical structure of the paper is stated as follows.l.This paper presents an investigation of stability and Hopf bifurcation of the Oregonator model with delay. First, we using the knowledge of dynamic systems to analyzed when D=0the Oregonator model with delay. Secondly, we systematically discussed the characteristic equation of positive equilibrium and occurrence of Hopf bifurcation.Thirdly, we explored the direction of the bifurcation and stability of bifurcating periodic solution by using the center manifold theorem and normal form method. Finally, inorder to support the theoretical predictions we use Matlab and DDE-Biftool to simulate the results.2.We explores a coupled Oregonator model. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. We also discussed the Z2equivariant property and the existence of multiple periodic solutions. Finally, we use numerical simulations to illustrate the results.