## Journal of Applied Mathematics

### Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting

#### Abstract

Two predator-prey models with nonmonotonic functional response and state-dependent impulsive harvesting are formulated and analyzed. By using the geometry theory of semicontinuous dynamic system, we obtain the existence, uniqueness, and stability of the periodic solution and analyse the dynamic phenomenon of homoclinic bifurcation of the first system by choosing the harvesting rate $\beta$ as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter $\delta$ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 803764, 11 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305639

Digital Object Identifier
doi:10.1155/2014/803764

Mathematical Reviews number (MathSciNet)
MR3191137

Zentralblatt MATH identifier
07010756

#### Citation

Huang, Mingzhan; Song, Xinyu. Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting. J. Appl. Math. 2014 (2014), Article ID 803764, 11 pages. doi:10.1155/2014/803764. https://projecteuclid.org/euclid.jam/1425305639

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