Belyakov homoclinic bifurcations in a tritrophic food chain model

Abstract

Complex dynamics of the most frequently used tritrophic food chain model are investigated in this paper. First it is shown that the model admits a sequence of pairs of Belyakov bifurcations (codimension-two homoclinic orbits to a critical node). Then fold and period-doubling cycle bifurcation curves associated to each pair of Belyakov points are computed and analyzed. The overall bifurcation scenario explains why stable limit cycles and strange attractors with dierent geometries can coexist. The analysis is conducted by combining numerical continuation techniques with theoretical arguments.