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Practical Numerical Algorithms for Chaotic Systems (Paperback, Softcover reprint of the original 1st ed. 1989)
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Practical Numerical Algorithms for Chaotic Systems (Paperback, Softcover reprint of the original 1st ed. 1989)
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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."
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