Periodic Fox production harvesting models with delay

We investigate the behavior of population models in a periodically varying environment. In this paper, we introduce the Fox surplus harvesting model with delayfrac(d N, d t) = N (t) fenced(r (t) ln^θ frac(K (t), N (g (t))) - F (t)) . We obtain explicit conditions for existence of global solutions, existence of a positive periodic solution, oscillation of all solutions about positive equilibrium and global attractivity of this equilibrium. Numerical simulations illustrate the effectiveness of the conditions for oscillations and stability of the Fox model. It was also found that oscillations in the intrinsic rate r(t) and the environmental carrying capacity K(t) contributed quantitatively and qualitatively to the system's dynamics in significant ways, and cannot be neglected in mathematical models of biological systems. Crown