一类扩散的Gierer-Meindardt的模型的振动模式和Hopf分支分析

Abstract

Abstract:

In this paper, a kind of diffusive Gierer-Meindardt model is considered. We performed detailed Hopf bifurcation analysis to this reaction diffusion systems. We not only prove the existence of Hopf bifurcations, but also derived the conditions to determine the bifurcation direction and the stability of the bifurcating periodic solutions. These results suggest the complex oscillatory patterns of this famous model. Computer simulations are included to support our theoretical analysis.

Key words: Gierer-Meindardt model, Hopf bifurcation, Oscillatory patterns, Stability, Bifurcation direction

CLC Number:

O189

Wan Aying, Yi Fengqi, Zheng Lifei. Hopf Bifurcation Analysis and Oscillatory Patterns of A Diffusive Gierer-Meinhardt Model[J].Acta mathematica scientia,Series A, 2015, 35(2): 381-394.

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Hopf Bifurcation Analysis and Oscillatory Patterns of A Diffusive Gierer-Meinhardt Model

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