Periodic solution of a bioeconomic fishery model by coincidence degree theory

Abstract

In this article we use coincidence degree theory to study the existence of a positive periodic solutions to the following bioeconomic model in fishery dynamics { d n d t = n ( r ( t ) ( 1 − n K ) − q ( t ) E n + D ) , d E d t = E ( A ( t ) q ( t ) α ( t ) n n + D − q 2 ( t ) α ( t ) n 2 E ( n + D ) 2 − c ( t ) ) , where the functions r , q , A , c and α are continuous positive T-periodic functions. This is the model of a coastal fishery represented as a single site with $n(t)$ is the fish stock biomass, and n(t) is the fishing effort. Examples are given to strengthen our results.