Nilpotent singularities and chaos: Tritrophic food chains

•Simple tools of local bifurcation theory are introduced to prove the existence of chaotic dynamics.•A simple algorithm is described.•Method is applied to prove the existence of strange attractors in two models of tritrophic food chains. Local bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding this method and describe the main steps to illustrate numerically the chaotic dynamics emerging near these nilpotent singularities. This is a general-purpose method and we hope it can be applied to a huge range of models.