Asymptotic stability of a modified Lotka-Volterra model with small immigrations

Abstract Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the det...

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Autores principales:	Takeru Tahara, Maica Krizna Areja Gavina, Takenori Kawano, Jerrold M. Tubay, Jomar F. Rabajante, Hiromu Ito, Satoru Morita, Genki Ichinose, Takuya Okabe, Tatsuya Togashi, Kei-ichi Tainaka, Akira Shimizu, Takashi Nagatani, Jin Yoshimura
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3e8cedea30a0486a948d3988c50cf953
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spelling	oai:doaj.org-article:3e8cedea30a0486a948d3988c50cf9532021-12-02T12:32:09ZAsymptotic stability of a modified Lotka-Volterra model with small immigrations10.1038/s41598-018-25436-22045-2322https://doaj.org/article/3e8cedea30a0486a948d3988c50cf9532018-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-25436-2https://doaj.org/toc/2045-2322Abstract Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.Takeru TaharaMaica Krizna Areja GavinaTakenori KawanoJerrold M. TubayJomar F. RabajanteHiromu ItoSatoru MoritaGenki IchinoseTakuya OkabeTatsuya TogashiKei-ichi TainakaAkira ShimizuTakashi NagataniJin YoshimuraNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-7 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Takeru Tahara Maica Krizna Areja Gavina Takenori Kawano Jerrold M. Tubay Jomar F. Rabajante Hiromu Ito Satoru Morita Genki Ichinose Takuya Okabe Tatsuya Togashi Kei-ichi Tainaka Akira Shimizu Takashi Nagatani Jin Yoshimura Asymptotic stability of a modified Lotka-Volterra model with small immigrations
description	Abstract Predator-prey systems have been studied intensively for over a hundred years. These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction. Thus, we have no solution for asymptotic stability in predator-prey systems, unlike most natural predator-prey interactions that sometimes exhibit stable and persistent coexistence. Here, we demonstrate that adding a small immigration into the prey or predator population can stabilize the LV system. Although LV systems have been studied intensively, there is no study on the non-linear modifications that we have tested. We also checked the effect of the inclusion of non-linear interaction term to the stability of the LV system. Our results show that small immigrations invoke stable convergence in the LV system with three types of functional responses. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.
format	article
author	Takeru Tahara Maica Krizna Areja Gavina Takenori Kawano Jerrold M. Tubay Jomar F. Rabajante Hiromu Ito Satoru Morita Genki Ichinose Takuya Okabe Tatsuya Togashi Kei-ichi Tainaka Akira Shimizu Takashi Nagatani Jin Yoshimura
author_facet	Takeru Tahara Maica Krizna Areja Gavina Takenori Kawano Jerrold M. Tubay Jomar F. Rabajante Hiromu Ito Satoru Morita Genki Ichinose Takuya Okabe Tatsuya Togashi Kei-ichi Tainaka Akira Shimizu Takashi Nagatani Jin Yoshimura
author_sort	Takeru Tahara
title	Asymptotic stability of a modified Lotka-Volterra model with small immigrations
title_short	Asymptotic stability of a modified Lotka-Volterra model with small immigrations
title_full	Asymptotic stability of a modified Lotka-Volterra model with small immigrations
title_fullStr	Asymptotic stability of a modified Lotka-Volterra model with small immigrations
title_full_unstemmed	Asymptotic stability of a modified Lotka-Volterra model with small immigrations
title_sort	asymptotic stability of a modified lotka-volterra model with small immigrations
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/3e8cedea30a0486a948d3988c50cf953
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Asymptotic stability of a modified Lotka-Volterra model with small immigrations

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