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Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity

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  • Liu, Chao
  • Wang, Luping
  • Zhang, Qingling
  • Yan, Yun

Abstract

This paper presents a double delayed bioeconomic phytoplankton zooplankton system with commercial harvesting on zooplankton and environmental stochasticity. Maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered. Environmental stochasticity is incorporated into the proposed system in form of Gaussian white noises. Some sufficient conditions are derived to show that the proposed system has a unique global positive solution. In absence of double time delays, stochastic stability and existence of stochastic Hopf bifurcation are studied based on invariant measure theory and singular boundary theory of diffusion process for the proposed system. In presence of double time delays, asymptotic behaviors of the interior equilibrium are discussed by constructing some appropriate Lyapunov functions.

Suggested Citation

  • Liu, Chao & Wang, Luping & Zhang, Qingling & Yan, Yun, 2017. "Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 682-698.
    • Handle: RePEc:eee:phsmap:v:482:y:2017:i:c:p:682-698
    DOI: 10.1016/j.physa.2017.04.104
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    Cited by:

    1. Wang, Jufeng & Zhou, MengChu & Liu, Chunfeng, 2018. "Stochastic stability of Markovian jump linear systems over networks with random quantization density and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1128-1139.
    2. Liu, Chao & Xun, Xinying & Zhang, Qingling & Li, Yuanke, 2019. "Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 99-118.
    3. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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