The Michelson system

Abstract

The Michelson system is a three dimension autonomous ODE system that arises in the context of studying the travelling waves solutions of the Kuramoto-Sivashinsky equation. Nonetheless, this system has its own relevance in itself, as it possesses some rich dynamics. In particular, the Michelson system is an interesting system to study since it is non-Hamiltonian, volume preserving and has a time reversing symmetry. In this work we will study the main properties of the system from a theoretical and a numerical point of view. More precisely, in the theoretical part we introduce the properties mentioned above and study the equilibrium points stability and their invariant manifolds. Moreover, some results on the existence of some type of orbits are also given. For the numerical part, we implement an algorithm to integrate orbits and give detailed methods to find periodic orbits. However, the main result of this block is the implementation of an algorithm to find the heteroclinic orbits of the Michelson system.