Dynamics of a stochastic hybrid delay one-predator-two-prey model with harvesting and jumps in a polluted environment

Sheng Wang; Baoli Lei; Sheng Wang; Baoli Lei

doi:10.3934/mmc.2025007

Mathematical Modelling and Control

2025, Volume 5, Issue 1: 85-102. doi: 10.3934/mmc.2025007

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Research article

Dynamics of a stochastic hybrid delay one-predator-two-prey model with harvesting and jumps in a polluted environment

Sheng Wang ^,,
Baoli Lei

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China

Received: 08 May 2024 Revised: 13 October 2024 Accepted: 25 October 2024 Published: 18 March 2025

This paper concerns the dynamics of a stochastic, hybrid delay, one-predator-two-prey model with harvesting and Lévy jumps in a polluted environment. Under some basic assumptions, sufficient conditions of stochastic persistence in the mean and extinction of each species are obtained, as well as the existence of optimal harvesting strategy (OHS). Our results show that both time delays and environmental noises affect the survival state of the species. Moreover, the accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Finally, some numerical simulations are provided to support our results.
- stochastic predator-prey model,
- Markovian switching,
- time delay,
- Lévy jump
Citation: Sheng Wang, Baoli Lei. Dynamics of a stochastic hybrid delay one-predator-two-prey model with harvesting and jumps in a polluted environment[J]. Mathematical Modelling and Control, 2025, 5(1): 85-102. doi: 10.3934/mmc.2025007

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Abstract

This paper concerns the dynamics of a stochastic, hybrid delay, one-predator-two-prey model with harvesting and Lévy jumps in a polluted environment. Under some basic assumptions, sufficient conditions of stochastic persistence in the mean and extinction of each species are obtained, as well as the existence of optimal harvesting strategy (OHS). Our results show that both time delays and environmental noises affect the survival state of the species. Moreover, the accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Finally, some numerical simulations are provided to support our results.

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