Nonlinear Dynamical Economics and Chaotic Motion - Hardcover

Lorenz, Hans-Walter

Hardcover

ISBN 10: 3540568816 ISBN 13: 9783540568810

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1993

Synopsis

Usually, the first edition of a book still contains a multiplicity of typographic, con- ceptional, and computational errors even if one believes the opposite at the time of publication. As this book did not represent a counterexample to this rule, the current second edition offers a chance to remove at least the known shortcomings. The book has been partly re-organized. The previously rather long Chapter 4 has been split into two separate chapters dealing with discrete-time and continuous- time approaches to nonlinear economic dynamics. The short summary of basic properties of linear dynamical systems has been banned to an appendix because the line of thought in the chapter seems to have been unnecessarily interrupted by these technical details and because the book concentrates on nonlinear systems. This appendix, which mainly deals with special formal properties of dynamical sys- tems, also contains some new material on invariant subspaces and center-manifold reductions. A brief introduction into the theory of lags and operators is followed by a few remarks on the relation between the 'true' properties of dynamical systems and their behavior observable in numerical experiments. Additional changes in the main part of the book include a re-consideration of Popper's determinism vs. inde- terminism discussion in the light of chaotic properties of deterministic, nonlinear systems in Chapter 1. An investigation of a simultaneous price-quantity adjustment process, a more detailed inquiry into the uniqueness property of limit cycles, and a short presentation of relaxation oscillations are included in Chapter 2.

About this title

Synopsis

This survey of recent developments in nonlinear economic dynamics describes mathematical topics such as the existence of endogenous fluctuations in low-dimensional dynamical systems, structural instability and bifurcations in discrete-time and continuous time systems, chaotic behaviour in deterministic nonlinear systems, statistical properties of nonlinear time series, and discontinuous motion in the form of elementary catastrophies. The book attempts to familiarize the reader with the available mathematical material and its potential relevance for economic theory. All formal results are illustrated with economic examples from diverse fields including business-cycle theory, descriptive and optimal growth theory, international-trade theory, and microeconomic adjustment processes. The major changes made in this second edition include a reorganization of parts of the text, a deepening of several mathematical concepts, and descriptions of a larger number of economic applications. As in the first edition, special emphasis is put on the didactical presentation of the new material.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1993
• Language: English
• ISBN 10: 3540568816
• ISBN 13: 9783540568810
• Binding: Hardcover
• Edition number: 2
• Number of pages: 336