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

Chao Liu, Luping Wang, Qingling Zhang and Yun Yan

Physica A: Statistical Mechanics and its Applications, 2017, vol. 482, issue C, 682-698

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.

Keywords: Maturation delay; Gestation delay; Environmental stochasticity; Economic interest; Stochastic Hopf bifurcation; Stability analysis (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:482:y:2017:i:c:p:682-698

DOI: 10.1016/j.physa.2017.04.104

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