Bogdanov-Takens Bifurcation in a Leslie Type Tritrophic Model with General Functional Responses

The dynamics of a differential system modeling a tritrophic food chain of Leslie type is analyzed. It is assumed that the prey has general growth rate and the predator (superpredator) population eats the prey (predator) through a general functional response. The parameter conditions that ensure a coexistence equilibrium point, where the differential system exhibits a codimension 2 Bogdanov-Takens bifurcation (BTb), is given. Some numerical examples where the functional responses are Holling type and the prey population has logistic growth rate are shown. The techniques that have been used to obtain these results may be applied to ecological models with other functional responses types.