MULTISTABILITY ON A LESLIE-GOWER TYPE PREDATOR-PREY MODEL WITH NONMONOTONIC FUNCTIONAL RESPONSE

In this work, a bidimensional continuous-time differential equations system is analyzed which is derived from a Leslie type predator-prey model by considering a nonmonotonic functional response (or Holling type IV or Monod Haldane). This functional response is employed to explain a class of prey antipredator strategies and we study how it influences in bifurcation and stability behavior of model. System obtained can have one, two or three equilibrium point at interior of the first quadrant, but here we describe the dynamics of the particular cases when system has one or two equilibrium points. Making a time rescaling we obtain a polynomial differential equations system topologically equivalent to original one and we prove that for certain subset of parameters, the model exhibits biestability phenomenon, since there exists an stable limit cycle surrounding two singularities of vector field one of these stable. We prove that there are conditions on the parameter values for which the unique equilibrium point at the first quadrant is stable and surrounded by two limit cycles, the innermost unstable and the outhermost stable. Also we show the existence of separatrix curves on the phase plane that divide the behavior of the trajectories, which have different omega-limit sets, and we have that solutions are highly sensitives to initial conditions. However, the populations always coexist since the singularity (0, 0) is a nonhyperbolic saddle point.