The interactions between two species are basic in the study of complex food chains, particularly the relation among the predators and their prey.The analysis of simple models, described by continuous-time systems, in which some ecological phenomena are incorporated giving lights about this interesting interrelationship.In this work, a Leslie-Gower type predator-prey model is analyzed, considering two aspects: the prey defends from the predation, forming group defense and the predators have an alternative food. So, a rational Holling type IV functional response and a modification of the predators carrying capacity are assumed, to describe each phenomenon.We determine conditions on the parameter space for the existence of the equilibria and their nature.Using the Lyapunov quantities method, we also establish conditions on the parameter values for which there exist a unique positive equilib...

The interactions between two species are basic in the study of complex food chains, particularly the relation among the predators and their prey.The analysis of simple models, described by continuous-time systems, in which some ecological phenomena are incorporated giving lights about this interesting interrelationship.In this work, a Leslie-Gower type predator-prey model is analyzed, considering two aspects: the prey defends from the predation, forming group defense and the predators have an alternative food. So, a rational Holling type IV functional response and a modification of the predators carrying capacity are assumed, to describe each phenomenon.We determine conditions on the parameter space for the existence of the equilibria and their nature.Using the Lyapunov quantities method, we also establish conditions on the parameter values for which there exist a unique positive equilib...