CODIMENSION-TWO BIFURCATION ANALYSIS OF THE CONTINUOUS STIRRED TANK REACTOR MODEL WITH DELAY

Ai Ke; Chunrui Zhang

doi:10.11948/2018.1586

2018 Volume 8 Issue 5

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Ai Ke, Chunrui Zhang. CODIMENSION-TWO BIFURCATION ANALYSIS OF THE CONTINUOUS STIRRED TANK REACTOR MODEL WITH DELAY[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1586-1603. doi: 10.11948/2018.1586

Citation:

Ai Ke, Chunrui Zhang. CODIMENSION-TWO BIFURCATION ANALYSIS OF THE CONTINUOUS STIRRED TANK REACTOR MODEL WITH DELAY[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1586-1603. doi: 10.11948/2018.1586

CODIMENSION-TWO BIFURCATION ANALYSIS OF THE CONTINUOUS STIRRED TANK REACTOR MODEL WITH DELAY

Department of Mathematics, Northeast Forestry University, Harbin, 150040, China

Fund Project:

Abstract

Abstract

The aim of this paper is to research the dynamical behaviors of the continuous stirred tank reactor (CSTR) model with delay. Firstly, we discuss the situation that its related characteristic equation has a simple zero root and a pair of purely imaginary roots. Secondly, the center manifold method and the normal form method are used to reduce the equation of CSTR model. Finally, some characteristics about the CSTR model can be obtained. We analyze three different topological structure and give entire bifurcation diagrams and phase portraits, which are innovative phenomenon. At the end, we obtain the stable and unstable periodic solutions by numerical simulation.
- Delay /
- CSTR model /
- normal form /
- Zero-Hopf bifurcation
MSC: 34C14;34K18

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References

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