Positive periodic solution of an augmented predator-prey model with seasonal harvest of prey and migration of predator

The present paper deals with an Holling-Type-II predator-prey model incorporating a seasonal harvest of the prey and migration of predator. The model describes the interaction between migratory bird population as the predator and the fish population as prey. Some sufficient conditions are obtained for permanence and global asymptotical stability of the system by using the comparison theorem and constructing a suitable Lyapunov function. By using the continuation theorem of coincidence degree theory, sufficient condition for existence of a positive periodic solution is established. Some computational results have been addressed.