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Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 6084-6109. doi: 10.3934/mbe.2023263
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Optimal harvesting strategy for stochastic hybrid delay Lotka-Volterra systems with Lévy noise in a polluted environment

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

  • Academic Editor: Xiaodi Li
  • Received: 21 September 2022 Revised: 13 December 2022 Accepted: 27 December 2022 Published: 31 January 2023

  • This paper concerns the dynamics of two stochastic hybrid delay Lotka-Volterra systems with harvesting and Lévy noise in a polluted environment (i.e., predator-prey system and competitive system). For every system, sufficient and necessary conditions for persistence in mean and extinction of each species are established. Then, sufficient conditions for global attractivity of the systems are obtained. Finally, sufficient and necessary conditions for the existence of optimal harvesting strategy are provided. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the dynamic behaviors and optimal harvesting strategy are closely correlated with both time delays and three types of environmental noises (namely white Gaussian noises, telephone noises and Lévy noises).

    Citation: Sheng Wang, Lijuan Dong, Zeyan Yue. Optimal harvesting strategy for stochastic hybrid delay Lotka-Volterra systems with Lévy noise in a polluted environment[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6084-6109. doi: 10.3934/mbe.2023263

    Related Papers:

  • This paper concerns the dynamics of two stochastic hybrid delay Lotka-Volterra systems with harvesting and Lévy noise in a polluted environment (i.e., predator-prey system and competitive system). For every system, sufficient and necessary conditions for persistence in mean and extinction of each species are established. Then, sufficient conditions for global attractivity of the systems are obtained. Finally, sufficient and necessary conditions for the existence of optimal harvesting strategy are provided. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the dynamic behaviors and optimal harvesting strategy are closely correlated with both time delays and three types of environmental noises (namely white Gaussian noises, telephone noises and Lévy noises).


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