The Holling-Tanner model considering an alternative food for predator.pdf

This work deals with a modified Leslie-Gower type predator-prey model where the predators have an alternative food when the quantity of prey diminish and a Holling type II functional response is considered.With both assumptions the model obtained has a significative difference with the known May-Holling-Tanner model, since the new equilibrium point appears, which can be a repeller or a saddle point for different set on the parameter spaceWe can obtain different dynamics according the parameter values and it can possible to prove that the existence of a unique positive equilibrium point which is global asymptotically stable.Also, for other parameter constraints we prove the existence of separatrix curves on the phase plane that divide the behaviour of the trajectories, which can have different ω − limit implying that solutions are highly sensitives to initial conditions.