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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 |
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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.
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Received: 10 April 2025
Revised: 25 June 2025
Accepted manuscript online: 01 July 2025
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PACS:
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05.10.Gg
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(Stochastic analysis methods)
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02.50.-r
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(Probability theory, stochastic processes, and statistics)
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12472033). |
Corresponding Authors:
You-Ming Lei
E-mail: leiyouming@nwpu.edu.cn
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Cite this article:
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 2026 Chin. Phys. B 35 010507
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