Predator-prey system: Prey's counter-attack on juvenile predators shows opposite side of the same ecological coin

The dynamics of a predator-prey model with stage-structure on predator and counterattacking behavior such that the prey can attack juvenile predator, is investigated in this paper. Adult predators may easily achieve success in overcoming prey strategies designed to protect themselves from attack but juvenile predators, which are in the learning stage of predation, may be vulnerable to counterattack by preys in self-defence due to their comparatively smaller size and eventually get killed. Our main objective is to understand how the dynamics of counter-attacking by the preys against juvenile predators help in its survival. Both exponential and logistic growth of the preys are considered in this investigation. In qualitative analysis, permanence, impermanence, and stabilities of all the equilibrium points of the system are discussed to investigate the dynamical behavior of the system. The inclusion of sub-critical and super-critical Hopf bifurcations makes the dynamics more interesting. The mathematical approaches advocated here complement and enhance the theoretical and numerical approaches applied to the system. (C) 2020 Elsevier Inc. All rights reserved.