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Hopf Bifurcation Analysis in the Coral Reef Delay Differential Equations (DDE) Model

DOI: 10.12677/AAM.2016.51005, PP. 31-40

Keywords: 珊瑚礁模型,时滞,Hopf分支,正周期解
Coral Reef Models
, Delay, Hopf Bifurcations, Periodic Solutions

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The dynamics of the coral reef DDE model is investigated. Li et al. [1] proved that a sequence of Hopf bifurcations occured at the positive equilibrium as the delay increased. In this paper, by applying the center manifold theorem and the normal form theory, we provide a detailed analysis of the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions at the positive equilibrium. Finally, focused parameters are obtained which determine property of the Hopf bifurcation and numerical calculation are given to justify the valid of the theoretical analysis.


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