Open AccessBifurcation analysis and optimal control of a delayed single-species fishery economic model
Author(s) -
Xin Gào,
Yue Zhang
Publication year - 2022
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.2022378
Subject(s) - hopf bifurcation , hoarding (animal behavior) , control theory (sociology) , bifurcation , speculation , profit (economics) , optimal control , mathematics , economics , mathematical optimization , control (management) , ecology , microeconomics , nonlinear system , physics , biology , finance , management , foraging , quantum mechanics
In this paper, a single-species fishery economic model with two time delays is investigated. The system is shown to be locally stable around the interior equilibrium when the parameters are in a specific range, and the Hopf bifurcation is shown occur as the time delays cross the critical values. Then the direction of Hopf bifurcation and the stability of bifurcated periodic solutions are discussed. In addition, the optimal cost strategy is obtained to maximize the net profit and minimize the waste by hoarding for speculation. We also design controls to minimize the waste by hoarding for the speculation of the system with time delays. The existence of the optimal controls and derivation from the optimality conditions are discussed. The validity of the theoretical results are shown via numerical simulation.