NUMERICAL CONTINUATION OF BRANCH POINTS OF EQUILIBRIA AND PERIODIC ORBITS

We consider the three-parameter numerical continuation of branch points in dynamical systems, with emphasis on the continuation of branch points of periodic orbits. We consider both, the case of branch points along one-parameter families of limit cycles (typical in systems with symmetry), and the case of branch points along fold-curves of limit cycles (typical in generic systems). We discuss new algorithms based on bordered matrices for both detection and continuation. We apply the techniques to a model of a chemical reactor, a model of an electronic circuit, and a model from celestial mechanics. Our algorithms have been implemented in freely available software.