Lyapunov stability for a class of predator-prey model with delayed nutrient recycling

A predator-prey model with nutrient recycling of distributed delay is proposed in this paper. The delay presents the taken time when the dead body of the predator is decomposed. The Lyapunov functional is constructed and used to investigate the stability at the positive equilibrium. As a special case, the model with nutrient recycling of discrete delay is easily obtained. The theoretical analysis is in agreement with that from the numerical simulation. The results show that a small delay can ensure the stability of the predator-prey system. This suggests that the predator-prey system can be always stable when the dead body is decomposed enough quickly.