DYNAMIC PROPERTIES OF THE OREGONATOR MODEL WITH DELAY

Xiang Wu; Chunrui Zhang

doi:10.11948/2012006

2012 Volume 2 Issue 1

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Xiang Wu, Chunrui Zhang. DYNAMIC PROPERTIES OF THE OREGONATOR MODEL WITH DELAY[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 91-102. doi: 10.11948/2012006

Citation:

Xiang Wu, Chunrui Zhang. DYNAMIC PROPERTIES OF THE OREGONATOR MODEL WITH DELAY[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 91-102. doi: 10.11948/2012006

DYNAMIC PROPERTIES OF THE OREGONATOR MODEL WITH DELAY

Department of Mathematics, Northeast Forestry University, Harbin 150040, P. R. China

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Abstract

Abstract

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 Matlab and DDE-Biftool.
- Delay /
- Oregonator model /
- stability /
- Hopf bifurcation
MSC: 34C23;37G15

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References

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