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Stochastic Gilpin-Ayala Model with Environmental Pollution and Markovian Switching |
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PP: 837-852 |
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doi:10.18576/amis/200320
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Author(s) |
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Youssef EL Khalfi,
Bilal Harchaoui,
Mouad Esseroukh,
Ouahib El Hanchi,
Bilal El Khatib,
Adel Settati,
Aadil Lahrouz,
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Abstract |
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| This study examines the stochastic Gilpin-Ayala model in a polluted environment, incorporating Markovian switching and white noise effects. The analysis establishes conditions under which the trivial equilibrium remains globally stable. Additionally, explicit criteria are derived to determine whether the population persists or faces extinction within this stochastic framework. The study also demonstrates the existence of a stationary distribution under specific conditions. Numerical simulations are carried out to validate the theoretical findings, providing empirical evidence and practical insights.
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