Stability of a time-varying fishing model with delay

Abstract To incorporate ecosystem effects, environmental variability and other factors that affect the population growth, the periodicity of the parameters of the model is assumed. We introduce a delay differential equation model which describes how fish are harvested: (A) N ( t ) = [ a ( t ) 1 + ( N ( θ ( t ) ) K ( t ) ) γ − b ( t ) ] N ( t ) . In our previous studies the persistence of Eq. (A) and the existence of a periodic solution to this equation were investigated. In the present paper the explicit conditions of global attractivity of the positive periodic solutions to Eq. (A) are obtained. It will also be shown that if the stability conditions are violated, the model exhibits sustained oscillations.