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

Authors

  • Zizhen Zhang School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, Anhui, 233030
  • Yugui Chu School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, Anhui, 233030
  • Xin Zhang School of Mathematics, Jilin University, Changchun, 130012

DOI:

https://doi.org/10.13447/j.1674-5647.2018.02.08

Keywords:

delay, Hopf bifurcation, predator-prey system, periodic solution, toxicity

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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Published

2019-12-16

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Issue

Vol. 34 No. 2 (2018)

Section

Articles

How to Cite

Hopf Bifurcation of Delayed Predator-Prey System with Reserve Area for Prey and in the Presence of Toxicity. (2019). Communications in Mathematical Research, 34(2), 161-170. https://doi.org/10.13447/j.1674-5647.2018.02.08