Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment
Abstract A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a proper Lyapunov function. Then the extinction property and its threshold between p...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-10-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03590-8 |
| _version_ | 1819026957397917696 |
|---|---|
| author | Li Wang |
| author_facet | Li Wang |
| author_sort | Li Wang |
| collection | DOAJ |
| description | Abstract A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a proper Lyapunov function. Then the extinction property and its threshold between persistence and extinction are discussed by using Itô’s formula and the strong law of large numbers of martingale, and the sufficient condition of a.s. exponential stability of equilibrium point is obtained. Finally, the conclusions are tested by several numerical simulations. |
| first_indexed | 2024-12-21T05:34:50Z |
| format | Article |
| id | doaj.art-5a0528ba03874d089421c68c10339a1e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-21T05:34:50Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-5a0528ba03874d089421c68c10339a1e2022-12-21T19:14:27ZengSpringerOpenAdvances in Difference Equations1687-18472021-10-012021111810.1186/s13662-021-03590-8Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environmentLi Wang0School of Mathematics and Statistics, Ningxia UniversityAbstract A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a proper Lyapunov function. Then the extinction property and its threshold between persistence and extinction are discussed by using Itô’s formula and the strong law of large numbers of martingale, and the sufficient condition of a.s. exponential stability of equilibrium point is obtained. Finally, the conclusions are tested by several numerical simulations.https://doi.org/10.1186/s13662-021-03590-8Lotka–Volterra food web systemPositive periodic solutionLyapunov functionExponential stability |
| spellingShingle | Li Wang Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment Advances in Difference Equations Lotka–Volterra food web system Positive periodic solution Lyapunov function Exponential stability |
| title | Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment |
| title_full | Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment |
| title_fullStr | Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment |
| title_full_unstemmed | Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment |
| title_short | Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment |
| title_sort | study on asymptotic behavior of stochastic lotka volterra system in a polluted environment |
| topic | Lotka–Volterra food web system Positive periodic solution Lyapunov function Exponential stability |
| url | https://doi.org/10.1186/s13662-021-03590-8 |
| work_keys_str_mv | AT liwang studyonasymptoticbehaviorofstochasticlotkavolterrasysteminapollutedenvironment |