Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching
Understanding the impact of unpredictable environmental fluctuations is crucial in population ecology because such fluctuations are an important feature of natural population systems. In this paper, we consider a stochastic single-species Kolmogorov system under Markovian switching. By using the Lya...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/5/784 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850030287912697856 |
|---|---|
| author | Zhixian Zhang Xiaoquan Ding |
| author_facet | Zhixian Zhang Xiaoquan Ding |
| author_sort | Zhixian Zhang |
| collection | DOAJ |
| description | Understanding the impact of unpredictable environmental fluctuations is crucial in population ecology because such fluctuations are an important feature of natural population systems. In this paper, we consider a stochastic single-species Kolmogorov system under Markovian switching. By using the Lyapunov method, we establish sufficient conditions for stochastic permanence, exponential ergodicity, and extinction of the system. Some examples are presented to illustrate corollaries, showing that our results generalize and improve on some known ones. |
| format | Article |
| id | doaj-art-a8fe64182bc44be1a347fd7f2a31c88a |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a8fe64182bc44be1a347fd7f2a31c88a2025-08-20T02:59:15ZengMDPI AGMathematics2227-73902025-02-0113578410.3390/math13050784Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian SwitchingZhixian Zhang0Xiaoquan Ding1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaUnderstanding the impact of unpredictable environmental fluctuations is crucial in population ecology because such fluctuations are an important feature of natural population systems. In this paper, we consider a stochastic single-species Kolmogorov system under Markovian switching. By using the Lyapunov method, we establish sufficient conditions for stochastic permanence, exponential ergodicity, and extinction of the system. Some examples are presented to illustrate corollaries, showing that our results generalize and improve on some known ones.https://www.mdpi.com/2227-7390/13/5/784stochastic single-species Kolmogorov systemMarkovian switchingstochastic permanencestationary distributionexponential ergodicityextinction |
| spellingShingle | Zhixian Zhang Xiaoquan Ding Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching Mathematics stochastic single-species Kolmogorov system Markovian switching stochastic permanence stationary distribution exponential ergodicity extinction |
| title | Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching |
| title_full | Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching |
| title_fullStr | Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching |
| title_full_unstemmed | Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching |
| title_short | Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching |
| title_sort | dynamics of a stochastic single species kolmogorov system under markovian switching |
| topic | stochastic single-species Kolmogorov system Markovian switching stochastic permanence stationary distribution exponential ergodicity extinction |
| url | https://www.mdpi.com/2227-7390/13/5/784 |
| work_keys_str_mv | AT zhixianzhang dynamicsofastochasticsinglespecieskolmogorovsystemundermarkovianswitching AT xiaoquanding dynamicsofastochasticsinglespecieskolmogorovsystemundermarkovianswitching |