Dynamic balance and reliability of a stochastic ecosystem with Markov switching

doi:10.1088/1674-1056/adea58

中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10507-010507.doi: 10.1088/1674-1056/adea58

Dynamic balance and reliability of a stochastic ecosystem with Markov switching

Ya-Nan Sun(孙雅楠)¹, Xin-Zhi Liu(刘新芝)², and You-Ming Lei(雷佑铭)^1,†

1 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China;
2 Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L, 3G1, Canada

收稿日期:2025-04-10 修回日期:2025-06-25 接受日期:2025-07-01 发布日期:2026-01-09
通讯作者: You-Ming Lei E-mail:leiyouming@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12472033).

Dynamic balance and reliability of a stochastic ecosystem with Markov switching

Ya-Nan Sun(孙雅楠)¹, Xin-Zhi Liu(刘新芝)², and You-Ming Lei(雷佑铭)^1,†

1 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China;
2 Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L, 3G1, Canada

Received:2025-04-10 Revised:2025-06-25 Accepted:2025-07-01 Published:2026-01-09
Contact: You-Ming Lei E-mail:leiyouming@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12472033).

摘要/Abstract

摘要： A stochastic predator-prey system with Markov switching is explored. We have developed a new chasing technique to efficiently solve the Fokker-Planck-Kolmogorov and backward Kolmogorov equations. Dynamic balance and reliability of the switching system are evaluated via stationary probability density function and first-passage failure theory, taking into account factors such as switching frequencies, noise intensities, and initial conditions. Results reveal that Markov switching leads to stochastic P-bifurcation, enhancing dynamic balance and reducing white-noise-induced oscillations. But frequent switching can heighten initial value dependence, harming reliability. Further, the influence of the subsystem on the switching system is not proportional to its action probabilities. Monte Carlo simulations validate the findings, offering an in-depth exploration of these dynamics.

关键词: Dynamic balance and reliability of a stochastic ecosystem with Markov switching

Abstract: A stochastic predator-prey system with Markov switching is explored. We have developed a new chasing technique to efficiently solve the Fokker-Planck-Kolmogorov and backward Kolmogorov equations. Dynamic balance and reliability of the switching system are evaluated via stationary probability density function and first-passage failure theory, taking into account factors such as switching frequencies, noise intensities, and initial conditions. Results reveal that Markov switching leads to stochastic P-bifurcation, enhancing dynamic balance and reducing white-noise-induced oscillations. But frequent switching can heighten initial value dependence, harming reliability. Further, the influence of the subsystem on the switching system is not proportional to its action probabilities. Monte Carlo simulations validate the findings, offering an in-depth exploration of these dynamics.

Key words: stochastic ecosystem, Markov switching, first-passage failure, reliability

中图分类号: (Stochastic analysis methods)

05.10.Gg

02.50.-r (Probability theory, stochastic processes, and statistics) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)

Ya-Nan Sun(孙雅楠), Xin-Zhi Liu(刘新芝), and You-Ming Lei(雷佑铭). Dynamic balance and reliability of a stochastic ecosystem with Markov switching[J]. 中国物理B, 2026, 35(1): 10507-010507.

Ya-Nan Sun(孙雅楠), Xin-Zhi Liu(刘新芝), and You-Ming Lei(雷佑铭). Dynamic balance and reliability of a stochastic ecosystem with Markov switching[J]. Chin. Phys. B, 2026, 35(1): 10507-010507.

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Dynamic balance and reliability of a stochastic ecosystem with Markov switching

Dynamic balance and reliability of a stochastic ecosystem with Markov switching

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