Analysis of Observed Chaotic Data
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Beschreibung
When I encountered the idea of chaotic behavior in deterministic dynami cal systems, it gave me both great pause and great relief. The origin of the great relief was work I had done earlier on renormalization group properties of homogeneous, isotropic fluid turbulence. At the time I worked on that, it was customary to ascribe the apparently stochastic nature of turbulent flows to some kind of stochastic driving of the fluid at large scales. It was simply not imagined that with purely deterministic driving the fluid could be turbulent from its own chaotic motion. I recall a colleague remarking that there was something fundamentally unsettling about requiring a fluid to be driven stochastically to have even the semblance of complex motion in the velocity and pressure fields. I certainly agreed with him, but neither of us were able to provide any other reasonable suggestion for the observed, apparently stochastic motions of the turbulent fluid. So it was with relief that chaos in nonlinear systems, namely, complex evolution, indistinguish able from stochastic motions using standard tools such as Fourier analysis, appeared in my bag of physics notions. It enabled me to have a physi cally reasonable conceptual framework in which to expect deterministic, yet stochastic looking, motions. The great pause came from not knowing what to make of chaos in non linear systems.
Bestselling title now available as inexpensive softcover * * Provides a toolkit of tried-and-tested methods for analyzing signals from nonlinear sources * Methods are applicable in physics, biology, geophysics, and control and communications engineering * Many illustrative examples
This book develops a clear and systematic treatment the sort of data one obtains from nonlinear systems. Emphasizing the use of the modern mathematical tools for investigating chaotic behavior to uncover properties of physical systems, the book requires knowledge of dynamical systems at the advanced undergraduate level.
Autor*in
Henry Abarbanel
Themen in »Analysis of Observed Chaotic Data«
Mathematica dynamical systems dynamics fractal geophysics information theory laser modeling noise physics stability