STUDY OF A NONLINEAR MODEL FOR TWO PREY AND TWO PREDATORS SPECIES

Abstract

   In this work we propose and analyze a model, where prey species is supposed to live in two distinct habitats with group defense. One of the predators tends to switch between the habitats. The boundedness of the positive solutions and local stability for all possible equilibrium points of the model are studied for the case, where the switching indicator is   furthermore, a suitable Lyapunov function has been defined to construct a basin of attraction for the interior equilibrium point. Numerical simulations are used to support the analytical results, such that some examples of locally stable and unstable equilibrium points furthermore stable limit cycle will be given.

 Key words: Prey, Predator, Switching, Group defense.