Open AccessGlobal analysis and optimal harvesting for a hybrid stochastic phytoplankton-zooplankton-fish model with distributed delays
Author(s) -
Yuan Xia,
Wei Zhou,
Zhi Yang
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020326
Subject(s) - mathematical optimization , markov chain , extinction (optical mineralogy) , stability (learning theory) , zooplankton , computer science , phytoplankton , brownian motion , control theory (sociology) , mathematics , environmental science , ecology , statistics , biology , artificial intelligence , paleontology , control (management) , machine learning , nutrient
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.