Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control

Spraying insecticides and releasing natural enemies are two commonly used methods in the integrated pest management strategy. With the rapid development of biotechnology, more and more realistic factors have been considered in the establishment and implementation of the integrated pest management mo...

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Autores principales:	Yuan Tian, Sanyi Tang
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	nonlinear impulsive poincarémap periodic solution existence and stability integrated pest management Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/bd0046d828224a87a846be961c2f787f
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spelling	oai:doaj.org-article:bd0046d828224a87a846be961c2f787f2021-11-23T01:53:21ZDynamics of a density-dependent predator-prey biological system with nonlinear impulsive control10.3934/mbe.20213621551-0018https://doaj.org/article/bd0046d828224a87a846be961c2f787f2021-08-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021362?viewType=HTMLhttps://doaj.org/toc/1551-0018Spraying insecticides and releasing natural enemies are two commonly used methods in the integrated pest management strategy. With the rapid development of biotechnology, more and more realistic factors have been considered in the establishment and implementation of the integrated pest management models, such as the limited resources, the mutual restriction between pests and natural enemies, and the monitoring data of agricultural insects. Given these realities, we have proposed a pest-natural enemy integrated management system, which is a nonlinear state-dependent feedback control model. Besides the anti-predator behavior of the pests to the natural enemies is considered, the density dependent killing rate of pests and releasing amount of natural enemies are also introduced into the system. We address the impulsive sets and phase sets of the system in different cases, and the analytic expression of the Poincaré map which is defined in the phase set was investigated. Further we analyze the existence, uniqueness, global stability of order-1 periodic solution. In addition, the existence of periodic solution of order-k (k≥2) is discussed. The theoretical analyses developed here not only show the relationship between the economic threshold and the other key factors related to pest control, but also reveal the complex dynamical behavior induced by the nonlinear impulsive control strategies.Yuan TianSanyi Tang AIMS Pressarticlenonlinear impulsivepoincarémapperiodic solutionexistence and stabilityintegrated pest managementBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 7318-7343 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonlinear impulsive poincarémap periodic solution existence and stability integrated pest management Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	nonlinear impulsive poincarémap periodic solution existence and stability integrated pest management Biotechnology TP248.13-248.65 Mathematics QA1-939 Yuan Tian Sanyi Tang Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
description	Spraying insecticides and releasing natural enemies are two commonly used methods in the integrated pest management strategy. With the rapid development of biotechnology, more and more realistic factors have been considered in the establishment and implementation of the integrated pest management models, such as the limited resources, the mutual restriction between pests and natural enemies, and the monitoring data of agricultural insects. Given these realities, we have proposed a pest-natural enemy integrated management system, which is a nonlinear state-dependent feedback control model. Besides the anti-predator behavior of the pests to the natural enemies is considered, the density dependent killing rate of pests and releasing amount of natural enemies are also introduced into the system. We address the impulsive sets and phase sets of the system in different cases, and the analytic expression of the Poincaré map which is defined in the phase set was investigated. Further we analyze the existence, uniqueness, global stability of order-1 periodic solution. In addition, the existence of periodic solution of order-k (k≥2) is discussed. The theoretical analyses developed here not only show the relationship between the economic threshold and the other key factors related to pest control, but also reveal the complex dynamical behavior induced by the nonlinear impulsive control strategies.
format	article
author	Yuan Tian Sanyi Tang
author_facet	Yuan Tian Sanyi Tang
author_sort	Yuan Tian
title	Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
title_short	Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
title_full	Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
title_fullStr	Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
title_full_unstemmed	Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
title_sort	dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/bd0046d828224a87a846be961c2f787f
work_keys_str_mv	AT yuantian dynamicsofadensitydependentpredatorpreybiologicalsystemwithnonlinearimpulsivecontrol AT sanyitang dynamicsofadensitydependentpredatorpreybiologicalsystemwithnonlinearimpulsivecontrol
_version_	1718417398789308416

Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control

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