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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/280945 |
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| _version_ | 1850225300567228416 |
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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. |
| format | Article |
| id | doaj-art-53c2e4dae9b847c382bb79164c8620fb |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |