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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 280945, 11 pages
http://dx.doi.org/10.1155/2013/280945
Research Article

Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China

Received 10 June 2013; Revised 23 August 2013; Accepted 2 September 2013

Academic Editor: Hamid Reza Karimi

Copyright © 2013 Xianghong Zhang and Sanyi Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Filippov ratio-dependent prey-predator model with economic threshold is proposed and studied. In particular, the sliding mode domain, sliding mode dynamics, and the existence of four types of equilibria and tangent points are investigated firstly. Further, the stability of pseudoequilibrium is addressed by using theoretical and numerical methods, and also the local sliding bifurcations including regular/virtual equilibrium bifurcations and boundary node bifurcations are studied. Finally, some global sliding bifurcations are addressed numerically. The globally stable touching cycle indicates that the density of pest population can be successfully maintained below the economic threshold level by designing suitable threshold policy strategies.