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2014 Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting
Mingzhan Huang, Xinyu Song
J. Appl. Math. 2014: 1-11 (2014). DOI: 10.1155/2014/803764

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 β as control parameter. Besides, we also study the homoclinic bifurcation of the second system about parameter δ on the basis of the theory of rotated vector field. Finally, numerical simulations are presented to illustrate the results.

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Mingzhan Huang. Xinyu Song. "Periodic Solutions and Homoclinic Bifurcations of Two Predator-Prey Systems with Nonmonotonic Functional Response and Impulsive Harvesting." J. Appl. Math. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/803764

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010756
MathSciNet: MR3191137
Digital Object Identifier: 10.1155/2014/803764

Rights: Copyright © 2014 Hindawi

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