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Catastrophes (Mathematics) --- Catastrophes (Mathematics).

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Catastrophes (Mathematics)

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Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it possible for anyone with a comparatively modest background in mathematics - no more than is usually included in a first year university course for students not specialising in the subject - to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it. Over half the book is devoted to applications, partly because it is not possible yet for the mathematician applying catastrophe theory to separate the analysis from the original problem. Most of these examples are drawn from the biological sciences, partly because they are more easily understandable and partly because they give a better illustration of the distinctive nature of catastrophe theory. This controversial and intriguing book will find applications as a text and guide to theoretical biologists, and scientists generally who wish to learn more of a novel theory.

Catastrophes (Mathematics)

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"Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided"--

Bifurcation theory --- Catastrophes (Mathematics)

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What is chaos? How can it be measured? How are the models estimated? What is catastrophe? How is it modelled? How are the models estimated? These questions are the focus of this volume.

Chaotic behavior in systems. --- Catastrophes (Mathematics)