Stability analysis of periodic Fox production models

In this paper we introduce a nonlinear Fox surplus production model in a periodic environment. The existence and stability of the periodic solutions of nonautonomous nonlinear differential equation (A) are analyzed. Sufficient conditions are obtained for the global attractivity of positive periodic solutions. Our results extend those the well-known results recently obtained by Brauer for a periodic Gompertzian model. We study the combined effects of periodically varying carrying capacity, inherent growth rates, and periodic harvesting of the population. Some numerical simulations illustrate how the Fox model is able to capture the trend in the data for Pacific Ocean perch obtained by the Pacific Biological Station (Nanaimo, BC).