Hopf Bifurcation of Delayed Predator-Prey System with Reserve Area for Prey and in the Presence of Toxicity
Year: 2018
Author: Zizhen Zhang, Yugui Chu, Xin Zhang
Communications in Mathematical Research , Vol. 34 (2018), Iss. 2 : pp. 161–170
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2018.02.08
Communications in Mathematical Research , Vol. 34 (2018), Iss. 2 : pp. 161–170
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: delay Hopf bifurcation predator-prey system periodic solution toxicity