Neimark–Sacker bifurcation in a tritrophic model with defense in the prey

Abstract We analyze a tritrophic discrete system. The analysis focuses in two cases, the two dimensional one in which the absence of super-predator lead to a predator-prey discrete system; secondly, we consider a model constructed using the average grow method in each density of the species. In both cases, we prove that the coexistence of species takes place by means of a supercritical Neimark–Sacker bifurcation at one of the fixed points that the system could have. We assume that the lowest trophic level has logistic grow and the functional responses for predators-prey and superpredator-mesopredator are Holling type IV.