Dynamic behaviors of a stage structure amensalism system with a cover for the first species
Abstract In this paper, we propose and study a two-species stage structured amensalism model with a cover for the first species. By developing a new analysis technique or, more precisely, by combining the differential inequality theory and the Lyapunov function method, we obtain sufficient condition...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1729-1 |
| _version_ | 1818521212453650432 |
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| author | Chaoquan Lei |
| author_facet | Chaoquan Lei |
| author_sort | Chaoquan Lei |
| collection | DOAJ |
| description | Abstract In this paper, we propose and study a two-species stage structured amensalism model with a cover for the first species. By developing a new analysis technique or, more precisely, by combining the differential inequality theory and the Lyapunov function method, we obtain sufficient conditions ensuring the global attractivity of positive and boundary equilibria, respectively. Our study shows that the final density of the first species is an increasing function of the partial cover, and if the stage structured species is globally asymptotically stable, then there exists a threshold such that if the cover is greater than this threshold, the species can still exist in the long run, whereas if the cover is too small, then the first species is driven to extinction. |
| first_indexed | 2024-12-11T01:48:03Z |
| format | Article |
| id | doaj.art-89a5f0905d0042aaa01db1d022d0ae86 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T01:48:03Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-89a5f0905d0042aaa01db1d022d0ae862022-12-22T01:24:50ZengSpringerOpenAdvances in Difference Equations1687-18472018-08-012018112310.1186/s13662-018-1729-1Dynamic behaviors of a stage structure amensalism system with a cover for the first speciesChaoquan Lei0Department of Mathematics, Ningde Normal UniversityAbstract In this paper, we propose and study a two-species stage structured amensalism model with a cover for the first species. By developing a new analysis technique or, more precisely, by combining the differential inequality theory and the Lyapunov function method, we obtain sufficient conditions ensuring the global attractivity of positive and boundary equilibria, respectively. Our study shows that the final density of the first species is an increasing function of the partial cover, and if the stage structured species is globally asymptotically stable, then there exists a threshold such that if the cover is greater than this threshold, the species can still exist in the long run, whereas if the cover is too small, then the first species is driven to extinction.http://link.springer.com/article/10.1186/s13662-018-1729-1Stage structureAmensalismLyapunov functionDifferential inequalityGlobal stability |
| spellingShingle | Chaoquan Lei Dynamic behaviors of a stage structure amensalism system with a cover for the first species Advances in Difference Equations Stage structure Amensalism Lyapunov function Differential inequality Global stability |
| title | Dynamic behaviors of a stage structure amensalism system with a cover for the first species |
| title_full | Dynamic behaviors of a stage structure amensalism system with a cover for the first species |
| title_fullStr | Dynamic behaviors of a stage structure amensalism system with a cover for the first species |
| title_full_unstemmed | Dynamic behaviors of a stage structure amensalism system with a cover for the first species |
| title_short | Dynamic behaviors of a stage structure amensalism system with a cover for the first species |
| title_sort | dynamic behaviors of a stage structure amensalism system with a cover for the first species |
| topic | Stage structure Amensalism Lyapunov function Differential inequality Global stability |
| url | http://link.springer.com/article/10.1186/s13662-018-1729-1 |
| work_keys_str_mv | AT chaoquanlei dynamicbehaviorsofastagestructureamensalismsystemwithacoverforthefirstspecies |