Nonlinear Physics And Chaos
Werner H. Lauterborn, Ulrich Parlitz · 1996
Abstract To be sure, our description of nature is far from being complete. However, we are improving constantly in many directions, one of them being nonlinear physics. Indeed, we have learned that nonlinearity introduces a wealth of genuine phenomena. Among them, chaotic dynamics is the most puzzling and intriguing one. This type of irregular dynamics calls for new methods to cope with and has already set our for applications. The investigations on chaotic dynamics have shed new light on the notions of predictability and determinism - and their relation -, quite fundamental issues. The deterministic dynamics of even simple systems may be notoriously difficult to predict and even impossible in the long run. Such systems abound in nature, and examples can be drawn from almost any scientific discipline (see, for instance, [1-71]). This tutorial and review presents an overview of the achievements and some present research activities in the field of nonlinear dynamics. In particular, questions of embedding data into high-dimensional spaces, of modelling and prediction, noise reduction, detecting determinism in time series, and secure communication via chaotic synchronization are addressed.