Practical Numerical Algorithms for Chaotic Systems

Parker, Thomas S.; Chua, Leon

ISBN 10: 0387966897 / ISBN 13: 9780387966892

Editore: Springer, 1991

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Titolo: Practical Numerical Algorithms for Chaotic ...

Casa editrice: Springer

Data di pubblicazione: 1991

Legatura: Rilegato

Condizione: Good

Descrizione articolo

Riassunto:

One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi­ neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci­ ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex­ pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin­ ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.

Contenuti:

Contents: Steady-State Solutions.- Poincaré Maps.- Stability.- Integration.- Locating Limit Sets.- Manifolds.- Dimension.- Bifurcation Diagrams.- Programming.- Phase Portraits.- The Newton-Raphson Algorithm.- The Variational Equation.- Differential Topology.- The Poincaré Map.- One Lyapunov Exponent Vanishes.- Cantor Sets.- List ot Symbols.- Bibliography.- Index.