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Klappentext One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex! nonlinear or chaotic! behavior. In this book! the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical! engineering! and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom! linear stability analysis of fixed points! nonlinear behavior of fixed points! bifurcation analysis! spatially distributed systems! broken symmetries! pattern formation! and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems! and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministic phase space descriptions. This book is suitable for senior undergraduate and graduate students taking nonlinear courses from many different perspectives including physics! chemistry! biology! and engineering. Zusammenfassung The aim of this book is to develop a unified approach to nonlinear science which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Inhaltsverzeichnis Preface; 1. Nonlinear behavior in the physical sciences and biology: some typical examples; 2. Quantitative formulation; 3. Dynamical systems with a finite number of degrees of freedom; 4. Linear stability analysis of fixed points; 5. Nonlinear behavior around fixed points: bifurcation analysis; 6. Spatially distributed systems, broken symmetries, pattern formation; 7. Chaotic dynamics; Appendices; References; Index.
