DYNAMIC PROPERTIES OF THE OREGONATOR MODEL WITH DELAY

作者：Wu Xiang; Zhang Chunrui^*

来源：Journal of Applied Analysis and Computation, 2012, 2(1): 91-102.

• Delay
• Oregonator model
• stability
• Hopf bifurcation

Delayed feedbacks are quite common in many physical and biological systems and in particular many physiological systems. Delay can cause a stable system to become unstable and vice versa. One of the well-studied non-biological chemical oscillators is the Belousov-Zhabotinsky(BZ) reaction. This paper presents an investigation of stability and Hopf bifurcation of the Oregonator model with delay. We analyze the stability of the equilibrium by using linear stability method. When the eigenvalues of the characteristic equation associated with the linear part are pure imaginary, we obtain the corresponding delay value. We find that stability of the steady state changes when the delay passes through the critical value. Then, we calculate the explicit formulae for determining the direction of the Hopf bifurcation and the stability of these periodic solutions bifurcating from the steady states, by using the normal form theory and the center manifold theorem. Finally, numerical simulations results are given to support the theoretical predictions by using Mat lab and DDE-Biftool.

• 出版日期2012
• 单位东北林业大学