The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate
Whether the integrated control measures are applied or not depends not only on the current density of pest population, but also on its current growth rate, and this undoubtedly brings challenges and new ideas to the state control measures that only rely on the pest density. To address this, utilizin...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6509867 |
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| author | Ihsan Ullah Khan Sanyi Tang Biao Tang |
| author_facet | Ihsan Ullah Khan Sanyi Tang Biao Tang |
| author_sort | Ihsan Ullah Khan |
| collection | DOAJ |
| description | Whether the integrated control measures are applied or not depends not only on the current density of pest population, but also on its current growth rate, and this undoubtedly brings challenges and new ideas to the state control measures that only rely on the pest density. To address this, utilizing the tactics of IPM, we constructed a Lotka-Volterra predator-prey system with action threshold depending on the pest density and its changing rate and examined its dynamical behavior. We present new criteria guaranteeing the existence, uniqueness, and global stability of periodic solutions. With the help of Lambert W function, the Poincaré map is constructed for the phase set, which can help us to provide the satisfactory conditions for the existence and stability of the semitrivial periodic solution and interior order-1 periodic solutions. Furthermore, the existence of order-2 and nonexistence of order-k(k≥3) periodic solutions are discussed. The idea of action threshold depending on the pest density and its changing rate is more general and can generate new remarkable directions as well compared with those represented in earlier studies. The analytical techniques developed in this paper can play a significant role in analyzing the impulsive models with complex phase set or impulsive set. |
| format | Article |
| id | doaj-art-8fee1b7cb3164c6ab65155a3fba7aca5 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8fee1b7cb3164c6ab65155a3fba7aca52025-02-03T06:05:06ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/65098676509867The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing RateIhsan Ullah Khan0Sanyi Tang1Biao Tang2School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaSchool of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaLaboratory for Industrial and Applied Mathematics (LIAM), York University, Toronto, M3J 1P3, CanadaWhether the integrated control measures are applied or not depends not only on the current density of pest population, but also on its current growth rate, and this undoubtedly brings challenges and new ideas to the state control measures that only rely on the pest density. To address this, utilizing the tactics of IPM, we constructed a Lotka-Volterra predator-prey system with action threshold depending on the pest density and its changing rate and examined its dynamical behavior. We present new criteria guaranteeing the existence, uniqueness, and global stability of periodic solutions. With the help of Lambert W function, the Poincaré map is constructed for the phase set, which can help us to provide the satisfactory conditions for the existence and stability of the semitrivial periodic solution and interior order-1 periodic solutions. Furthermore, the existence of order-2 and nonexistence of order-k(k≥3) periodic solutions are discussed. The idea of action threshold depending on the pest density and its changing rate is more general and can generate new remarkable directions as well compared with those represented in earlier studies. The analytical techniques developed in this paper can play a significant role in analyzing the impulsive models with complex phase set or impulsive set.http://dx.doi.org/10.1155/2019/6509867 |
| spellingShingle | Ihsan Ullah Khan Sanyi Tang Biao Tang The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate Complexity |
| title | The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate |
| title_full | The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate |
| title_fullStr | The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate |
| title_full_unstemmed | The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate |
| title_short | The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate |
| title_sort | state dependent impulsive model with action threshold depending on the pest density and its changing rate |
| url | http://dx.doi.org/10.1155/2019/6509867 |
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