An example of chaotic dynamics in 3D systems via stretching along paths

Abstract

We extend the concept of linked twist maps to a 3D setting and develop a global geometrical method to detect the presence of complex dynamics. Our approach, which is based on a recent variant of the theory of topological horseshoes, provides an analytical proof of “chaos” which does not involve small/large parameter techniques and is robust with respect to small perturbations. An application is given to a predator-prey system in $${{\mathbb R}^3}$$ with a Beddington-DeAngelis functional response.