Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model

In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and numerical simulation. Firstly, the mean-square stab...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Wen Liu, Jianfeng Feng
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	resilience reactivity amplification envelope ratio-dependent predator–prey model asymptotic and transient dynamics Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6b7e5791efaa42fc832b2c72bf34e7d3
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:6b7e5791efaa42fc832b2c72bf34e7d3
record_format	dspace
spelling	oai:doaj.org-article:6b7e5791efaa42fc832b2c72bf34e7d32021-11-11T18:19:06ZAnalysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model10.3390/math92127762227-7390https://doaj.org/article/6b7e5791efaa42fc832b2c72bf34e7d32021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2776https://doaj.org/toc/2227-7390In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and numerical simulation. Firstly, the mean-square stability matrix can be calculated from the Kronecker product, so as to compute three indicators (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the response to perturbation for the studied ecosystem. Since the above-measured amounts cannot be obtained explicitly, we use numerical simulation to draw the changing figures within the appropriate parameter range. Then we obtain some conclusions by comparing the numerical results. When perturbing any populations, increasing the disturbance intensity will reduce the mean-square stable area of the system. Ecologists can manage the ecosystem, reduce losses and maximize benefits according to the numerical results of the root-mean-square amplification envelope.Wen LiuJianfeng FengMDPI AGarticleresiliencereactivityamplification enveloperatio-dependent predator–prey modelasymptotic and transient dynamicsMathematicsQA1-939ENMathematics, Vol 9, Iss 2776, p 2776 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	resilience reactivity amplification envelope ratio-dependent predator–prey model asymptotic and transient dynamics Mathematics QA1-939
spellingShingle	resilience reactivity amplification envelope ratio-dependent predator–prey model asymptotic and transient dynamics Mathematics QA1-939 Wen Liu Jianfeng Feng Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model
description	In this paper, we focus on the asymptotic and transient dynamics of the studied ecosystem and measure the response to perturbation of the stochastic ratio-dependent predator–prey model. The method we use is mainly based on the Kronecker product and numerical simulation. Firstly, the mean-square stability matrix can be calculated from the Kronecker product, so as to compute three indicators (root-mean-square resilience, root-mean-square reactivity and root-mean-square amplification envelope) of the response to perturbation for the studied ecosystem. Since the above-measured amounts cannot be obtained explicitly, we use numerical simulation to draw the changing figures within the appropriate parameter range. Then we obtain some conclusions by comparing the numerical results. When perturbing any populations, increasing the disturbance intensity will reduce the mean-square stable area of the system. Ecologists can manage the ecosystem, reduce losses and maximize benefits according to the numerical results of the root-mean-square amplification envelope.
format	article
author	Wen Liu Jianfeng Feng
author_facet	Wen Liu Jianfeng Feng
author_sort	Wen Liu
title	Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model
title_short	Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model
title_full	Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model
title_fullStr	Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model
title_full_unstemmed	Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model
title_sort	analysis of asymptotic and transient behaviors of stochastic ratio-dependent predator–prey model
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/6b7e5791efaa42fc832b2c72bf34e7d3
work_keys_str_mv	AT wenliu analysisofasymptoticandtransientbehaviorsofstochasticratiodependentpredatorpreymodel AT jianfengfeng analysisofasymptoticandtransientbehaviorsofstochasticratiodependentpredatorpreymodel
_version_	1718431890938003456

Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model

Ejemplares similares