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

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 a...

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Main Authors: Xianghong Zhang, Sanyi Tang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/280945
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author Xianghong Zhang
Sanyi Tang
author_facet Xianghong Zhang
Sanyi Tang
author_sort Xianghong Zhang
collection DOAJ
description 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.
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spelling doaj-art-53c2e4dae9b847c382bb79164c8620fb2025-08-20T02:05:24ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/280945280945Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy ControlXianghong Zhang0Sanyi Tang1College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, ChinaCollege of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, ChinaThe 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.http://dx.doi.org/10.1155/2013/280945
spellingShingle Xianghong Zhang
Sanyi Tang
Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control
Abstract and Applied Analysis
title Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control
title_full Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control
title_fullStr Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control
title_full_unstemmed Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control
title_short Filippov Ratio-Dependent Prey-Predator Model with Threshold Policy Control
title_sort filippov ratio dependent prey predator model with threshold policy control
url http://dx.doi.org/10.1155/2013/280945
work_keys_str_mv AT xianghongzhang filippovratiodependentpreypredatormodelwiththresholdpolicycontrol
AT sanyitang filippovratiodependentpreypredatormodelwiththresholdpolicycontrol