Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems
In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extincti...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/4627571 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553699040296960 |
|---|---|
| author | Chunjin Wei Yingjie Fu |
| author_facet | Chunjin Wei Yingjie Fu |
| author_sort | Chunjin Wei |
| collection | DOAJ |
| description | In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations. |
| format | Article |
| id | doaj-art-9a1084f654294b9fb0bffd1690b75b32 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9a1084f654294b9fb0bffd1690b75b322025-02-03T05:53:25ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/46275714627571Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton SystemsChunjin Wei0Yingjie Fu1School of Sciences, Jimei University, Xiamen 361021, ChinaSchool of Sciences, Jimei University, Xiamen 361021, ChinaIn this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations.http://dx.doi.org/10.1155/2020/4627571 |
| spellingShingle | Chunjin Wei Yingjie Fu Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems Complexity |
| title | Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems |
| title_full | Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems |
| title_fullStr | Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems |
| title_full_unstemmed | Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems |
| title_short | Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems |
| title_sort | stationary distribution and periodic solution of stochastic toxin producing phytoplankton zooplankton systems |
| url | http://dx.doi.org/10.1155/2020/4627571 |
| work_keys_str_mv | AT chunjinwei stationarydistributionandperiodicsolutionofstochastictoxinproducingphytoplanktonzooplanktonsystems AT yingjiefu stationarydistributionandperiodicsolutionofstochastictoxinproducingphytoplanktonzooplanktonsystems |