The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate
Joint Authors
Tang, Sanyi
Khan, Ihsan Ullah
Tang, Biao
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-06-23
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Khan, Ihsan Ullah& Tang, Sanyi& Tang, Biao. 2019. The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate. Complexity،Vol. 2019, no. 2019, pp.1-15.
https://search.emarefa.net/detail/BIM-1132497
Modern Language Association (MLA)
Khan, Ihsan Ullah…[et al.]. The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate. Complexity No. 2019 (2019), pp.1-15.
https://search.emarefa.net/detail/BIM-1132497
American Medical Association (AMA)
Khan, Ihsan Ullah& Tang, Sanyi& Tang, Biao. The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate. Complexity. 2019. Vol. 2019, no. 2019, pp.1-15.
https://search.emarefa.net/detail/BIM-1132497
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1132497