| Citation: |
Jingyi Zhao, Zongbin Yin, Yongchang Wei, Jinhai Guo. STOCHASTIC ANALYSIS OF A GENERAL HOLLING TYPE PREDATOR-PREY MODEL WITH REGIME-SWITCHING AND HABITAT COMPLEXITY[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 636-664. doi: 10.11948/20250131
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STOCHASTIC ANALYSIS OF A GENERAL HOLLING TYPE PREDATOR-PREY MODEL WITH REGIME-SWITCHING AND HABITAT COMPLEXITY
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Abstract
This paper examines a generic predator-prey model of the Holling type that takes into account habitat complexity and Markovian chains. We first establish the existence and uniqueness of a global positive solution through rigorous stochastic analysis. Subsequently, we derive sharp threshold conditions governing population persistence and extinction, revealing that while moderate environmental noise may enhance species survival, excessive stochasticity inevitably leads to population collapse. Furthermore, we prove the existence of a unique stationary distribution by constructing appropriate Lyapunov functionals. Finally, the results of the numerical simulations are presented in order to illustrate the experimental findings.
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References
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Jingyi Zhao, Zongbin Yin, Yongchang Wei, Jinhai Guo. STOCHASTIC ANALYSIS OF A GENERAL HOLLING TYPE PREDATOR-PREY MODEL WITH REGIME-SWITCHING AND HABITAT COMPLEXITY[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 636-664. doi: 10.11948/20250131
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Figure 1.
(a) The movement of the Markov chain
$ \gamma(t) $ $ y(t) $ $ y(t) $ $ y(t) $ -
Figure 2.
The simulation of the prey
$ x(t) $ $ x_1(t) $ -
Figure 3.
(a) The movement of the Markov chain
$ \gamma(t) $ $ x(t) $ $ x(t) $ $ x(t) $ -
Figure 4.
(a) The movement of the Markov chain
$ \gamma(t) $ $ x(t) $ $ x(t) $ $ x(t) $ $ x(t) $ $ x(t) $ $ y(t) $ $ y(t) $