Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments

Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments

We address the question of the long-term coexistence of three competing species whose dynamics are governed by the partial differential equations. We obtain criteria for permanent coexistence in a Lotka-Volterra system modeling the interaction of three competing species in a bounded habitat whose ex...

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Main Authors: Benlong Xu, Zhenzhang Ni
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/376919
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spelling doaj-ec601cc5cbcb4615a9403f5576a1d1c02020-11-24T20:44:14ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/376919376919Permanence of Diffusive Models for Three Competing Species in Heterogeneous EnvironmentsBenlong Xu0Zhenzhang Ni1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaWe address the question of the long-term coexistence of three competing species whose dynamics are governed by the partial differential equations. We obtain criteria for permanent coexistence in a Lotka-Volterra system modeling the interaction of three competing species in a bounded habitat whose exterior is lethal to each species. It is also proved that if the intercompeting strength is very weak, the system is always permanent, provided that each single one of the three species can survive in the absence of the two other species.http://dx.doi.org/10.1155/2014/376919
collection DOAJ
language English
format Article
sources DOAJ
author Benlong Xu
Zhenzhang Ni
spellingShingle Benlong Xu
Zhenzhang Ni
Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments
Abstract and Applied Analysis
author_facet Benlong Xu
Zhenzhang Ni
author_sort Benlong Xu
title Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments
title_short Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments
title_full Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments
title_fullStr Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments
title_full_unstemmed Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments
title_sort permanence of diffusive models for three competing species in heterogeneous environments
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We address the question of the long-term coexistence of three competing species whose dynamics are governed by the partial differential equations. We obtain criteria for permanent coexistence in a Lotka-Volterra system modeling the interaction of three competing species in a bounded habitat whose exterior is lethal to each species. It is also proved that if the intercompeting strength is very weak, the system is always permanent, provided that each single one of the three species can survive in the absence of the two other species.
url http://dx.doi.org/10.1155/2014/376919
work_keys_str_mv AT benlongxu permanenceofdiffusivemodelsforthreecompetingspeciesinheterogeneousenvironments
AT zhenzhangni permanenceofdiffusivemodelsforthreecompetingspeciesinheterogeneousenvironments
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