Tracking sustained chaos

Tracking unstable periodic states first introduced in [Schwartz & Triandaf, 1992] is the process of continuing unstable solutions as a systems parameter is varied in experiments. The tracked dynamical objects have been periodic saddles of well-defined finite periods. However, other saddles, such as chaotic saddles, have not been successfully "tracked," or continued. In this paper, we introduce a new yet simple method which can be used to track chaotic saddles in dynamical systems, which allows an experimentalist to sustain chaotic transients far away from crisis parameter values. The method is illustrated on a periodically driven CO2 laser.