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Analysis and Simulation of Chaotic Systems (Hardcover, 2nd ed. 2000)
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Analysis and Simulation of Chaotic Systems (Hardcover, 2nd ed. 2000)
Series: Applied Mathematical Sciences, 94
Expected to ship within 12 - 19 working days
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Beginning with realistic mathematical or verbal models of physical
or biological phenomena, the author derives tractable mathematical
models that are amenable to further mathematical analysis or to
elucidating computer simulations. For the most part, derivations
are based on perturbation methods. Because of this, the majority of
the text is devoted to careful derivations of implicit function
theorems, the method of averaging, and quasi-static state
approximation methods. The duality between stability and
perturbation is developed and used, relying heavily on the concept
of stability under persistent disturbances. This explains why
stability results developed for quite simple problems are often
useful for more complicated, even chaotic, ones. Relevant topics
about linear systems, nonlinear oscillations, and stability methods
for difference, differential-delay, integro- differential and
ordinary and partial differential equations are developed
throughout the book. For the second edition, the author has
restructured the chapters, placing special emphasis on introductory
materials in Chapters 1 and 2 as distinct from presentation
materials in Chapters 3 through 8. In addition, more material on
bifurcations from the point of view of canonical models, sections
on randomly perturbed systems, and several new computer simulations
have been added.
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