Download PDF by John H. Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich: An Exploration of Dynamical Systems and Chaos

By John H. Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich

ISBN-10: 3662460424

ISBN-13: 9783662460429

This publication is conceived as a finished and unique text-book on non-linear dynamical structures with specific emphasis at the exploration of chaotic phenomena. The self-contained introductory presentation is addressed either to people who desire to examine the physics of chaotic structures and non-linear dynamics intensively in addition to people who find themselves curious to benefit extra in regards to the attention-grabbing global of chaotic phenomena. uncomplicated thoughts like Poincaré part, iterated mappings, Hamiltonian chaos and KAM idea, unusual attractors, fractal dimensions, Lyapunov exponents, bifurcation idea, self-similarity and renormalisation and transitions to chaos are completely defined. To facilitate comprehension, mathematical techniques and instruments are brought briefly sub-sections. The textual content is supported through a variety of laptop experiments and a mess of graphical illustrations and color plates emphasising the geometrical and topological features of the underlying dynamics.

This quantity is a totally revised and enlarged moment variation which contains lately got study result of topical curiosity, and has been prolonged to incorporate a brand new part at the uncomplicated innovations of chance thought. a very new bankruptcy on absolutely constructed turbulence provides the successes of chaos conception, its obstacles in addition to destiny tendencies within the improvement of complicated spatio-temporal structures.

"This ebook may be of worthwhile support for my lectures"  Hermann Haken, Stuttgart

"This text-book shouldn't be lacking in any introductory lecture on non-linear platforms and deterministic chaos" Wolfgang Kinzel, Würzburg

“This good written publication represents a entire treatise on dynamical platforms. it will probably function reference ebook for the entire box of nonlinear and chaotic platforms and experiences in a different manner on clinical advancements of modern many years in addition to very important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky collage Oldenburg, Germany

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Extra info for An Exploration of Dynamical Systems and Chaos

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A priori, because no assumption needs to be made about the type of these equations. , 2011). As a result, one obtains stochastic differential equations which contain both a deterministic and a stochastic part. However, in the following, we restrict our considerations to dynamical systems which can be described solely by deterministic equations. In the literature, a multitude of possible methods for characterising the occurrence of chaotic motions is presented. Apart from the power spectrum and autocorrelation, the two classic tools, we propose to concentrate on the following criteria: Lyapunov exponents, dimensions and Kolmogorov-Sinai entropy.

8). The recorded time series, which are evaluated in this method by means of a Fourier analysis, yield clearly defined peaks in the power spectrum diagram for periodic or quasi-periodic motions; in contrast, continuous curves or curves with a high noise level indicate chaotic or stochastic behaviour. This means that in the erratic case, the measured variables can no longer be represented as a discrete superposition of oscillations: from a critical value of this state variable in the Fourier-transformed signal onwards, a very high noise component in the spectrum emerges.

Chaotic responses of non-linear dynamical systems are almost a matter of course to us today. We draw attention to the appearance of such phenomena in a pendulum with a large amplitude and particularly so in the case of spatial oscillations. The well-known Duffing equation is another example. A further historical example is the well-known anorganic chemical reaction of Belousov-Zhabotinsky which offers a memorable display of colour. Yet the most impressive and still the most mysterious is the onset and development of turbulence in a fluid.

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An Exploration of Dynamical Systems and Chaos by John H. Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich

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