The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control
The idea of action threshold depends on the pest density and its change rate is more general and furthermore can produce new modelling techniques related to integrated pest management (IPM) as compared with those that appeared in earlier studies, which definitely bring challenges to analytical analy...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/4561241 |
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| author | Ihsan Ullah Khan Sanyi Tang |
| author_facet | Ihsan Ullah Khan Sanyi Tang |
| author_sort | Ihsan Ullah Khan |
| collection | DOAJ |
| description | The idea of action threshold depends on the pest density and its change rate is more general and furthermore can produce new modelling techniques related to integrated pest management (IPM) as compared with those that appeared in earlier studies, which definitely bring challenges to analytical analysis and generate new ideas to the state control measures. Keeping this in mind, using the strategies of IPM, we develop a prey-predator system with action threshold depending on the pest density and its change rate, and study its dynamical behavior. We develop new criteria guaranteeing the existence, uniqueness, local and global stability of order-1 periodic solutions. Applying the properties of Lambert W function, the Poincaré map is portrayed for the exact phase set, which is helpful to provide the sufficient conditions for the existence and stability of the interior order-1 periodic solutions and boundary order-1 periodic solution, also confirmed by numerical simulations. It is studied in detail that how and under what conditions the fixed point of Poincaré map and its stability are affected by the newly introduced action threshold. The analytical methods developed in this paper will be very beneficial to study other generalized models with state-dependent feedback control. |
| format | Article |
| id | doaj-art-fc1bd1c3674240a2b0a7b826d549afa5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fc1bd1c3674240a2b0a7b826d549afa52025-02-03T06:43:51ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/45612414561241The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback ControlIhsan Ullah Khan0Sanyi Tang1School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaSchool of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaThe idea of action threshold depends on the pest density and its change rate is more general and furthermore can produce new modelling techniques related to integrated pest management (IPM) as compared with those that appeared in earlier studies, which definitely bring challenges to analytical analysis and generate new ideas to the state control measures. Keeping this in mind, using the strategies of IPM, we develop a prey-predator system with action threshold depending on the pest density and its change rate, and study its dynamical behavior. We develop new criteria guaranteeing the existence, uniqueness, local and global stability of order-1 periodic solutions. Applying the properties of Lambert W function, the Poincaré map is portrayed for the exact phase set, which is helpful to provide the sufficient conditions for the existence and stability of the interior order-1 periodic solutions and boundary order-1 periodic solution, also confirmed by numerical simulations. It is studied in detail that how and under what conditions the fixed point of Poincaré map and its stability are affected by the newly introduced action threshold. The analytical methods developed in this paper will be very beneficial to study other generalized models with state-dependent feedback control.http://dx.doi.org/10.1155/2020/4561241 |
| spellingShingle | Ihsan Ullah Khan Sanyi Tang The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control Discrete Dynamics in Nature and Society |
| title | The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control |
| title_full | The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control |
| title_fullStr | The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control |
| title_full_unstemmed | The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control |
| title_short | The Impulsive Model with Pest Density and Its Change Rate Dependent Feedback Control |
| title_sort | impulsive model with pest density and its change rate dependent feedback control |
| url | http://dx.doi.org/10.1155/2020/4561241 |
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