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Nonlinear dynamical economics and chaotic motion. 2nd, rev. and enl. ed. (English) Zbl 0841.90036

Berlin: Springer-Verlag. xv, 319 p. (1993).
[For a review of the first ed. (1989) see Zbl 0717.90001.]
Many important processes in economies are inherently nonlinear as are shown by business cycles and fluctuations. However, the techniques for analyzing nonlinear dynamic systems are far less developed than linear models. This book aims at mending such an unfortunate state, and is designed as a survey of recent developments in dynamic systems theory and its applications to many economic problems. More specifically, the purpose of the book is to let economists make familiar with the existing literature in dynamic systems theory rather than to provide a complete overview from a mathematical point of view. Thus, the exposition assembles mathematical theorems, sometimes without proofs but with references to the sources in which proofs may be found.
This book consists of eight chapters. The first chapter shows that dynamic economics is greatly influenced by the mechanistic world view of the 18th and 19th centuries. It also gives the reader a short survey of linear dynamic systems in economics. Chapter 2 deals with basic topics for analyzing nonlinear dynamic systems such as the Poincaré-Bendixson theorem and the uniqueness of limit cycles. Chapter 3 turns to bifurcation theory which has been a major focus of research in economic dynamics during the last decade. Chapters 4 and 5 respectively discuss chaotic dynamics in discrete-time economic models and in continuous-time economic models. Chapter 6 is concerned with the empirically important question of establishing chaos in observed time series. Chapter 7 presents an outline of catastrophe theory and its applications to economics. Some concluding remarks are contained in Chapter 8.
In conclusion, this book is a useful and timely book for anyone who finds interest in economic dynamics and fluctuations. It contains amazingly many figures (133 figures!) which seem to greatly contribute to the charm of the subject.
Reviewer: Y.Sakai (Ibaraki)

MSC:

91B62 Economic growth models
91B84 Economic time series analysis
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming

Citations:

Zbl 0717.90001
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