Threshold analysis of a switched fishery model with stage structure and fishing moratorium

Abstract

Considering that fishing activities are forbidden during fishing moratorium and permitted after fishing moratorium, a fishery model with stage structure and fishing moratorium is formulated by a switched system which is composed of two subsystems, one does not have the term of harvest and the other one has the term of proportional harvest. After discussing the relations between two subsystems, the range of parameters considered in this paper is determined. The threshold condition for the stability of the switch system is given by a discrete system and Jury conditions. The region where the solutions tend to or are away from the common equilibrium is given by qualitative analyses. The positive periodic solution is also discussed. Finally, numerical simulations are given to verify the theoretical results and some discussions including the optimal problem are also given.