CONTROLLING CHAOS IN SYSTEMS WITH O(2) SYMMETRY

Methods for controlling chaos which use small parameter perturbations to stabilise a fixed point assume the existence of an isolated hyperbo lic fixed point. For maps with continuous symmetries, fixed points occ ur on continuous group orbits and so are not isolated and the linearis ation at a fixed point has an eigenvalue of +1 corresponding to pertur bations along the group orbit and so the fixed points are not hyperbol ic. In order to apply methods for controlling chaos in such systems, w e consider the map restricted to the orbit space and derive the parame ter perturbations from this orbit space map. This approach is applied to maps with O(2) symmetry. An example illustrates stabilisation of a fixed point and a drifting fixed point. (C) 1998 Elsevier Science Ltd. All rights reserved.