Abstract

Radical new developments have recently shown that tiny perturbations may be harnessed to control chaotic behaviour. The basic idea involving control of chaos is the stabilization of unstable periodic orbits embedded within a chaotic attractor. Since these orbits are very dense in such an attractor, a successful control of them may therefore serve as a generator of rich forms of periodic waves, so turning the presence of chaos to advantage. This strategy equally well applies to stabilizing unstable fixed points so giving steady-state behaviour. Based on this idea various control algorithms have been explored in which a fractional amount of the chaotic signal from the system, after being appropriately processed, is fed back to the system itself. Among these control algorithms, the OGY scheme¹ and OPF approach² are the two that have been most widely implemented in a wide arrange of chaotic systems in various branches of nonlinear science.³ Electronic circuits were used almost exclusively in these experimental realization for achieving appropriate signal differencing and synchronisation for the feedback, two essential criteria for the control. Recently, a control scheme is using continuous self-controlling feedback (CSC) was proposed and demonstrated,⁴ which comprises a simpler control algorithm in these sense that signal sychronisation can be automatically achieved and so only different signal between the chaotic output and itself, when delayed, is needed for dynamical control.

© 1994 IEEE