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Nonlinear economic dynamics. 4th, compl. rev. and enl. ed. (English) Zbl 0931.91024
Berlin: Springer. x, 288 p. (1997).
For earlier editions see Zbl 0695.90002 (1st ed. 1989) and Zbl 0827.90029 (3rd ed. 1993).
This book is devoted to nonlinear dynamic methods that are useful for economic analysis. This edition has been completely revised and enlarged. A substantial portion of topics related to spatial economics that appeared in previous editions has been removed and replaced by discussions on the dynamics of monopoly and oligopoly.
The book consists of 8 chapters. The first chapter provides an overview of the concepts and methods covered in the book. Chapter 2 is devoted to a review of methods of differential equations. It covers such topics as phase diagrams, structural stability, bifurcation, and perturbation methods. Chapter 3 is devoted to iterated maps of difference equations. The topics covered include the logistic map, Lyapunov exponent, symbolic dynamics, the Hénon model and the Mandelbrot set.
Chapters 4 and 5 explore the search process involving a monopolist in order to extract information about the demand curve, as well as the cyclic dynamics of the Cournot and Stackelberg models.
Chapters 6-8 are devoted to continuous-time and discrete-time business-cycle models. Chapter 6 focuses on the continuous-time multiplier-accelerator model and two-region model. Chapter 7 focuses on such models as inter-regional trade models that can be described by partial differential equations. Chapter 8 focuses on the chaotic dynamics of the nonlinear discrete-time multiplier-accelerator model. This book is useful to economists interested in finding explicit examples of applications of nonlinear dynamics to economics.
Reviewer: S.C.Hu (Nankang)

91B62 Economic growth models
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
37N40 Dynamical systems in optimization and economics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior