Existence and global stability of positive periodic solution of tri-trophic food chain with middle predator migratory in nature

Abstract

Predator avoidance is the most important factor inducing vertical migration among zooplankton. Light intensity at the surface water also plays an important role to shape the predation pressure on zooplankton as most of the fishes show visually oriented predation. In the present paper, we assume that zooplankton can switch between vulnerable and invulnerable state through vertical migration. This switching is regulated by light intensity, predator abundance and food abundance in surface water. We propose a tri-trophic food chain model incorporating migratory behavior of middle predator. Further, we study the non-autonomous version of the proposed model by incorporating the seasonal variation of the rate parameters of the model. The sufficient conditions for the existence of positive periodic solutions are obtained. We also obtain the conditions for the global attractivity of positive periodic solutions. The numerical experiments are carried out to substantiate analytical findings.