Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control

Xin Zhao; Lijun Wang; Pankaj Kumar Tiwari; He Liu; Yi Wang; Jianbing Li; Min Zhao; Chuanjun Dai; Qing Guo; Xin Zhao; Lijun Wang; Pankaj Kumar Tiwari; He Liu; Yi Wang; Jianbing Li; Min Zhao; Chuanjun Dai; Qing Guo

doi:10.3934/mbe.2023692

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 15496-15523. doi: 10.3934/mbe.2023692

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Research article

Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control

1.
College of Life and Environmental Science, Wenzhou University, Wenzhou 325035, China
2.
School of Intelligent Manufacturing and Vehicle Engineering, Sichuan Institute of Industrial Technology, Deyang 618500, China
3.
Department of Basic Science and Humanities, Indian Institute of Information Technology, Bhagalpur 813210, India
4.
College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China
5.
Environmental Engineering Program, University of Northern British Columbia, Prince George V2N 4Z9, Canada
6.
WZU-UNBC Joint Research Institute of Ecology and Environment, Wenzhou University, Wenzhou 325035, China
7.
National & Local Joint Engineering Research Center for Ecological Treatment Technology of Urban Water Pollution, Wenzhou University, Wenzhou 325035, China

Academic Editor: Yang Kuang

Received: 06 May 2023 Revised: 03 July 2023 Accepted: 04 July 2023 Published: 26 July 2023

In this paper, we investigate a stochastic nutrient-plankton model with impulsive control of the nutrient concentration and zooplankton population. Analytically, we find that the population size is nonnegative for a sufficiently long time. We derive some sufficient conditions for the existence of stable periodic oscillations, which indicate that the plankton populations will behave periodically. The numerical results show that the plankton system experiences a transition from extinction to the coexistence of species due to the emergence of impulsive control. Additionally, we observe that the nutrient pulse has a stronger relationship with phytoplankton growth than the zooplankton pulse. Although the frequency of impulsive control and appropriate environmental fluctuations can promote the coexistence of plankton populations, an excessive intensity of noise can result in the collapse of the entire ecosystem. Our findings may provide some insights into the relationships among nutrients, phytoplankton and zooplankton in a stochastic environment.
- nutrient-plankton model,
- pulse perturbations,
- stochastic fluctuation,
- positive T-periodic solutions
Citation: Xin Zhao, Lijun Wang, Pankaj Kumar Tiwari, He Liu, Yi Wang, Jianbing Li, Min Zhao, Chuanjun Dai, Qing Guo. Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 15496-15523. doi: 10.3934/mbe.2023692

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Abstract

In this paper, we investigate a stochastic nutrient-plankton model with impulsive control of the nutrient concentration and zooplankton population. Analytically, we find that the population size is nonnegative for a sufficiently long time. We derive some sufficient conditions for the existence of stable periodic oscillations, which indicate that the plankton populations will behave periodically. The numerical results show that the plankton system experiences a transition from extinction to the coexistence of species due to the emergence of impulsive control. Additionally, we observe that the nutrient pulse has a stronger relationship with phytoplankton growth than the zooplankton pulse. Although the frequency of impulsive control and appropriate environmental fluctuations can promote the coexistence of plankton populations, an excessive intensity of noise can result in the collapse of the entire ecosystem. Our findings may provide some insights into the relationships among nutrients, phytoplankton and zooplankton in a stochastic environment.

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