A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model
Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/7903450 |
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| author | Ihsan Ullah Khan Saif Ullah Ebenezer Bonyah Basem Al Alwan Ahmed Alshehri |
| author_facet | Ihsan Ullah Khan Saif Ullah Ebenezer Bonyah Basem Al Alwan Ahmed Alshehri |
| author_sort | Ihsan Ullah Khan |
| collection | DOAJ |
| description | Based on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models. |
| format | Article |
| id | doaj-art-babf7f6fbb5043a7817072091dbfc24b |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-babf7f6fbb5043a7817072091dbfc24b2025-02-03T01:29:14ZengWileyComplexity1099-05262022-01-01202210.1155/2022/7903450A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy ModelIhsan Ullah Khan0Saif Ullah1Ebenezer Bonyah2Basem Al Alwan3Ahmed Alshehri4Department of MathematicsDepartment of MathematicsDepartment of Mathematics EducationChemical Engineering DepartmentDepartment of MathematicsBased on the Lotka–Volterra system, a pest-natural enemy model with nonlinear feedback control as well as nonlinear action threshold is introduced. The model characterizes the implementation of comprehensive prevention and control measures when the pest density reaches the nonlinear action threshold level depending on the pest density and its change rate. The mortality rate of the pest is a saturation function that strictly depends on their density while the release of natural enemies is also a nonlinear pulse term depending on the density of real-time natural enemies. The exact impulsive and phase sets are given. The definition and properties of the Poincaré map corresponding to the pulse points on the phase set are provided. We investigate the existence and stability of boundary and interior order-1 periodic solution. The theoretical analysis developed in the present paper combined with nonlinear controlling measures as well as nonlinear action threshold methods and techniques laid the foundation for the establishment and analysis of other state-dependent feedback control models.http://dx.doi.org/10.1155/2022/7903450 |
| spellingShingle | Ihsan Ullah Khan Saif Ullah Ebenezer Bonyah Basem Al Alwan Ahmed Alshehri A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model Complexity |
| title | A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model |
| title_full | A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model |
| title_fullStr | A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model |
| title_full_unstemmed | A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model |
| title_short | A State-Dependent Impulsive Nonlinear System with Ratio-Dependent Action Threshold for Investigating the Pest-Natural Enemy Model |
| title_sort | state dependent impulsive nonlinear system with ratio dependent action threshold for investigating the pest natural enemy model |
| url | http://dx.doi.org/10.1155/2022/7903450 |
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