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Title: Dynamical analysis in a bioeconomic phytoplankton zooplankton system with double time delays and environmental stochasticity
Authors: Liu, C 
Wang, LP
Zhang, QL
Yan, Y
Keywords: Maturation delay
Gestation delay
Environmental stochasticity
Economic interest
Stochastic Hopf bifurcation
Stability analysis
Issue Date: 2017
Publisher: North-Holland
Source: Physica A. Statistical mechanics and its applications, 2017, v. 482, p. 682-698 How to cite?
Journal: Physica A. Statistical mechanics and its applications 
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.
ISSN: 0378-4371
EISSN: 1873-2119
DOI: 10.1016/j.physa.2017.04.104
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