数学研究通讯

2018, v.34(02) 161-170

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Hopf Bifurcation of Delayed Predator-prey System with Reserve Area for Prey and in the Presence of Toxicity
Hopf Bifurcation of Delayed Predator-prey System with Reserve Area for Prey and in the Presence of Toxicity

Zhang Zi-zhen;Chu Yu-gui;Zhang Xin;

摘要(Abstract):

A kind of three species delayed predator-prey system with reserve area for prey and in the presence of toxicity is proposed in this paper. Local stability of the coexistence equilibrium of the system and the existence of a Hopf bifurcation is established by choosing the time delay as the bifurcation parameter. Explicit formulas to determine the direction and stability of the Hopf bifurcation are obtained by means of the normal form theory and the center manifold theorem. Finally, we give a numerical example to illustrate the obtained results.

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基金项目(Foundation): The NSF(1608085QF151 and 1608085QF145)of Anhui Province

作者(Author): Zhang Zi-zhen;Chu Yu-gui;Zhang Xin;

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