Periodic Orbit Continuation in Multiple Time Scale Systems

Continuation methods utilizing boundary value solvers are an effective tool for computing unstable periodic orbits of dynamical systems. Auto [7] is the standard implementation of these procedures. Unfortunately, the collocation methods used in Auto often require very fine meshes for convergence on problems with multiple time scales. This inconvenience prompts the search for alternative methods for computing such periodic orbits; we introduce here new multiple-shooting algorithms based on geometric singular perturbation theory.