Tracking unstable phenomena in chaotic laser experiments: Extending regions of stability in a multimode laser

Abstract

Recently, experimental systems which exhibit chaos have been controlled using techniques such as OGY [1] and the related occasional proportional feedback, OPF [2]. The methods have been able to stabilize both low dimensional experiments, such as electronic circuits [2] as well as high dimensional multimode chaotic lasers [3]. Controlling a chaotic system consists of stabilizing an unstable steady state or periodic orbit by having the system perform small amplitude fluctuations about some fixed parameter value. The OPF method is implemented by choosing the fluctuations so that the system is brought closer to the unstable orbit of interest. In the OGY method, the fluctuations are chosen so that the iterates fall on the stable manifold of the unstable orbit, thus keeping the dynamics in the neighborhood of the point of interest in phase space. Both methods are clearly related [4].