Nonlinear Dynamical Economics and Chaotic Motion

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.

Klappentext

The book provides a survey of recent developments in nonlinear economic dynamics. Bifurcation theory and the emergence of chaotic motion in dynamic economic models is presented in a comprehensive and accessible though nevertheless thorough style. The reader can use the book as an introduction to nonlinear economic dynamics and as a reference to more advanced material. The major changes made in the second edition include a re-organization 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.

Inhalt

1. Economic Dynamics, Linearities, and the Classical Mechanistic Worldview.- 1.1. Some Reflections on the Origin of Economic Dynamics.- 1.2. The Deterministic Worldview and Deterministic Theories.- 1.3. The Dominance of Linear Dynamical Systems in Economics.- 2. Nonlinearities and Economic Dynamics.- 2.1. Preliminary Concepts.- 2.2. The Poincaré-Bendixson Theorem.- 2.3. The Uniqueness of Limit Cycles.- 2.4. Predator-Prey Models.- 2.5. Relaxation Oscillations.- 2.6. Irreversibility and Determinism in Dynamical Systems.- 3. Bifurcation Theory and Economic Dynamics.- 3.1. Preliminaries and Different Concepts of Structural Stability.- 3.2. Local Bifurcations in Continuous-Time Dynamical Systems.- 3.3. Local Bifurcations in Discrete-Time Dynamical Systems.- 4. Chaotic Dynamics in Discrete-Time Economic Models.- 4.1. Chaos in One-Dimensional, Discrete-Time Dynamical Systems.- 4.2. Chaos in Higher-Dimensional Discrete-Time Systems.- 4.3. Complex Transients in Discrete-Time Dynamical Systems.- 5. Chaotic Dynamics in Continuous-Time Economic Models.- 5.1. Basic Ideas.- 5.2. The Coupling of Oscillators.- 5.3. The Forced Oscillator.- 5.4. Homoclinic Orbits and Spiral-Type Attractors.- 6. Numerical Tools.- 6.1. Spectral Analysis.- 6.2. Dimension, Entropy, and Lyapunov Exponents.- 6.3. Are Economic Time Series Chaotic?.- 6.4. Predictability in the Face of Chaotic Dynamics.- 7. Catastrophe Theory and Economic Dynamics.- 7.1. Basic Ideas.- 7.2. The Kaldor Model in the Light of Catastrophe Theory.- 7.3. A Catastrophe-Theoretical Approach to Stagflation.- 8. Concluding Remarks.- A.1. Basic Properties of Linear Dynamical Systems.- A.2. Center Manifolds and the Reduction of (Effective) Dimensions.- A.3. A Brief Introduction to the Theory of Lags and Operators.- A.4. Numerical Simulationsand Chaotic Dynamics in Theoretical Economics.- References.- Name Index.