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DY: Dynamik und Statistische Physik

DY 40: Nonlinear dynamics III

DY 40.1: Hauptvortrag

Donnerstag, 27. März 2003, 09:30–10:00, G\"OR/226

Control of chaos by time-delayed feedback: a survey of theoretical and experimental aspects — •Wolfram Just — Institut für Physik, TU Chemnitz, 09107 Chemnitz

During the last decade control of chaos, i.e. the stabilisation of unstable periodic states by tiny control forces, has developed into one of the prominent topics in applied nonlinear science. The emphasis of noninvasive control schemes, where the control forces vanish asymptotically, opens the perspective to use control schemes for system analysis as well. While traditional control concepts are either confined to the stabilisation of time independent states or require some information about the underlying dynamics, time-delayed feedback control generates suitable control forces just from the time-delayed difference of a measured signal. Such a concept is simple to implement in quite different experimental contexts like magnetic, optical or chemical systems. But a deeper theoretical understanding of such control schemes requires a sound analysis of the corresponding delay-differential equations which constitute an inherently infinite-dimensional dynamical system. The talk presents an overview of recent theoretical results for time-delayed feedback control and of corresponding illustrations in different experimental contexts.