CONTROLLING CHAOS IN HIGH DIMENSIONS - THEORY AND EXPERIMENT

The main contribution of this work is the development of a high-dimens ional chaos control method that is effective, robust against noise, an d easy to implement in experiment. Assuming no knowledge of the model equations, the method achieves control by stabilizing a desired unstab le periodic orbit with any number of unstable directions, using small time-dependent perturbations of a single system parameter. Specificall y, our major results are as follows. First, we derive explicit control laws for time series produced by discrete maps. Second, we show how t o apply this control law to continuous-time problems by introducing st raightforward ways to extract from a continuous-time series a discrete time series that measures the dynamics of some Poincare map of the or iginal system. Third, we illustrate our approach with two examples of high-dimensional ordinary differential equations, one autonomous and t he other periodically driven. Fourth, we present the result on our suc cessful control of chaos in a high-dimensional experimental system, de monstrating the viability of the method in practical applications.