Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton

He Liu; Chuanjun Dai; Hengguo Yu; Qing Guo; Jianbing Li; Aimin Hao; Jun Kikuchi; Min Zhao; He Liu; Chuanjun Dai; Hengguo Yu; Qing Guo; Jianbing Li; Aimin Hao; Jun Kikuchi; Min Zhao

doi:10.3934/mbe.2021206

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 4101-4126. doi: 10.3934/mbe.2021206

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Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton

1.
School of Life and Environmental Science, Wenzhou University, Wenzhou 325035, China
2.
National & Local Joint Engineering Research Center for Ecological Treatment Technology of Urban Water Pollution, Wenzhou University, Wenzhou 325035, China
3.
Environmental Engineering Program, University of Northern British Columbia, 3333 University Way, Prince George, BC, V2N 4Z9, Canada
4.
WZU-UNBC Joint Research Institute of Ecology and Environment, Wenzhou University, Wenzhou 325035, China
5.
RIKEN Center for Sustainable Resource Science, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan

Academic Editor: Juan Luis García Guirao

Received: 15 March 2021 Accepted: 29 April 2021 Published: 11 May 2021

Environmental stochasticity and toxin-producing phytoplankton (TPP) are the key factors that affect the aquatic ecosystems. To investigate the effects of environmental stochasticity and TPP on the dynamics of plankton populations, a stochastic phytoplankton-zooplankton system with two TPP is studied theoretically and numerically in this paper. Theoretically, we first prove that the system possesses a unique and global positive solution with positive initial values, and then derive some sufficient conditions guaranteeing the extinction and persistence in the mean of the system. Significantly, it is shown that the system has a stationary distribution when toxin liberation rate reaches some a critical value. Additionally, numerical analysis shows that the white noise can affect the survival of plankton populations directly. Furthermore, it has been observed that the increasing one toxin liberation rate can increase the survival chance of phytoplankton and reduce the biomass of zooplankton, but the combined effects of two liberation rates on the changes in plankton populations are stronger than that of controlling any one of the two TPP.
- toxin-producing phytoplankton,
- phytoplankton-zooplankton system,
- white noise,
- extinction,
- stationary distribution
Citation: He Liu, Chuanjun Dai, Hengguo Yu, Qing Guo, Jianbing Li, Aimin Hao, Jun Kikuchi, Min Zhao. Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 4101-4126. doi: 10.3934/mbe.2021206

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Abstract

Environmental stochasticity and toxin-producing phytoplankton (TPP) are the key factors that affect the aquatic ecosystems. To investigate the effects of environmental stochasticity and TPP on the dynamics of plankton populations, a stochastic phytoplankton-zooplankton system with two TPP is studied theoretically and numerically in this paper. Theoretically, we first prove that the system possesses a unique and global positive solution with positive initial values, and then derive some sufficient conditions guaranteeing the extinction and persistence in the mean of the system. Significantly, it is shown that the system has a stationary distribution when toxin liberation rate reaches some a critical value. Additionally, numerical analysis shows that the white noise can affect the survival of plankton populations directly. Furthermore, it has been observed that the increasing one toxin liberation rate can increase the survival chance of phytoplankton and reduce the biomass of zooplankton, but the combined effects of two liberation rates on the changes in plankton populations are stronger than that of controlling any one of the two TPP.

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