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Nonlinear system theory

Nonlinear theories. --- System analysis. --- Network theory --- Systems analysis --- Nonlinear problems --- Nonlinearity (Mathematics) --- System theory --- Mathematical optimization --- Calculus --- Mathematical analysis --- Mathematical physics --- Network analysis --- Network science --- Nonlinear theories --- Analyse de systèmes --- Théories non linéaires --- ELSEVIER-B EPUB-LIV-FT --- System analysis

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Why does time seem to fly on some occasions and drag on others? Why do some societies seem more prone to totalitarianism than others? Why does atonal music sound "worse" to most of us than traditional music? How can a butterfly in Brazil affect the weather in Alaska? The set of ingenious interdisciplinary approaches that are, together, called the science of complexity offers answers to these and dozens of other questions that beg the larger question of why our universe seems so paradoxical. John L. Casti, renowned mathematician and science writer, argues that a complexity that defies human logic is only natural, and he shows directly, engagingly, and with a wealth of illustrations how complexity arises and how it works. Casti explores several types of phenomena that have, until now, consistently eluded science's attempts to understand them: the catastrophic, where a tiny change in a system produces a huge effect (as happens in earthquakes or political revolutions); the chaotic, which includes odd correlations like the ones that make predicting the weather or the stock market so difficult; paradox, in which you follow a commonsense rule and still something weird happens (the more lanes you add to the freeway, for example, the bigger the traffic jams); the irreducible, where, as in novels, symphonies and baseball games, the whole is greater than the sum of its parts; the emergent, in which a pattern, like life itself, seems to arise from out of nowhere. These phenomena encompass many of the most fascinating and important events and processes in science, the arts, nature, the economy, and everyday life. With authority and wit, this myth-shattering book explains how science is at last shedding light on some of the most perennially mystifying phenomena. It also offers a groundbreaking primer in what Casti calls "the science of surprise, " a revolutionary approach to solving a welter of mysteries great and small.

Chaotic behavior in systems. --- Paradox. --- Chaos --- Paradoxe

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Numerical solutions of differential equations --- Boundary value problems --- Initial value problems --- Invariant imbedding. --- Functional equations --- Invariants --- Mathematical physics --- Radiation --- Problems, Initial value --- Differential equations --- Boundary conditions (Differential equations) --- Functions of complex variables --- Data processing. --- Invariant imbedding --- Data processing --- Embeddings (Mathematics) --- Plongements (mathématiques) --- Boundary value problems - Data processing --- Initial value problems - Data processing