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Updated: Dec 3, 2025

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
Published on: July 30, 2019
Global analysis and optimal harvesting for a hybrid stochastic phytoplankton-zooplankton-fish model with distributed
Yuan Pei Xia1, Wei Song Zhou2, Zhi Chun Yang1
1School of Mathematical Sciences, Chongqing Normal University, Chongqing 401131, China.
Abstract:
In this paper, we formulate a phytoplankton-zooplankton-fish model with distributed delays and hybrid stochastic noises involving Brownian motion and Markov chain, and propose an optimal harvesting problem pursuing the maximum of total economic income. By global analysis in terms of some system parameters, we investigate the dynamical behaviors on the well-posedness, bounded- ness, persistence, extinction, stability and attractiveness of the solutions for the stochastic delayed system. Moreover, we provide sufficient and necessary condition ensuring the existence of the optimization solution for the optimization problem and obtain the optimal harvesting effect and the maximum of sustainable yield. Lastly, two numerical examples and their simulations are given to illustrate the effectiveness of our results.
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