Controlling chaos in low- and high-dimensional systems with periodic parametric perturbations

The effect of applying a periodic perturbation to an accessible parameter o f various chaotic systems is examined. Numerical results indicate that pert urbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively sma ll perturbations. Such perturbations can also control or significantly redu ce the dimension of high-dimensional systems. Initial application to the co ntrol of fluctuations in a prototypical magnetic fusion plasma device will be reviewed. [S1063-651X(99)11505-8].