Dynamics of adaptive systems

Abstract

A simple adaptive control mechanism is introduced into nonlinear systems that are capable of complicated oscillatory states and chaotic dynamics. It is shown that it provides efficient regulation while displaying novel behavior. Sudden perturbations in the system's parameters can degenerate into chaotic bursts with no precursors. When such bursts occur, the system first reverberates wildly and then recovers in times that are inversely proportional to the stiffness of the control. Also exhibited is a general control principle which provides a quantitative relation between the maximum amplitude of a perturbation from which a system can recover, and the speed at which it does so.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>