Dynamics of a Stochastic Single-Species Kolmogorov System Under Markovian Switching

Zhixian Zhang and Xiaoquan Ding ()
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Zhixian Zhang: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Xiaoquan Ding: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China

Mathematics, 2025, vol. 13, issue 5, 1-13

Abstract: 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.

Keywords: stochastic single-species Kolmogorov system; Markovian switching; stochastic permanence; stationary distribution; exponential ergodicity; extinction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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