Attractors, Bifurcations, & Chaos: Nonlinear Phenomena in Economics

ISBN-13: 9783642072963 / Angielski / Miękka / 2010 / 549 str.

Puu, Tönu

Opis

The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics," first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems," and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica." The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics," was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics chapters -on partial differential equations, and on bifurcations and catastrophe theory -thus making the mathematical background material fairly complete. The author is happy that this new book did rather well, but he preferred to rewrite it, rather than having just a new print run. Material, stemming from the first versions, was more than ten years old, while nonlinear dynamics has been a fast developing field, so some analyses looked rather old-fashioned and pedestrian. The necessary revision turned out to be rather substantial."

Recenzje

From the reviews of the second edition:

"Its unifying theme is the analysis of economic dynamics when we drop the assumptions of linearity and use the results of recently developing nonlinear dynamic science. ... the book is carefully organized and written in a friendly style. It is interesting and smooth reading. ... It is useful to graduate students, researchers and academics ... . The book is written in a readable fashion, all details are explained clearly. Therefore, the book is a must for anyone interested in nonlinear economic dynamics." (Akio Matsumoto, Journal of Economic Behavior and Organization, Vol. 58, 2005)

Spis treści

1 Introduction.- 2 Differential Equations: Ordinary.- 3 Differential Equations: Partial.- 4 Iterated Maps or Difference Equations.- 5 Bifurcation and Catastrophe.- 6 Monopoly.- 7 Duopoly and Oligopoly.- 8 Business Cycles: Continuous Time.- 9 Business Cycles: Continuous Space.- 10 Business Cycles: Discrete Time.- 11 Dynamics of Interregional Trade.- 12 Development: Increasing Complexity.- 13 Development: Multiple Attractors.- References.- List of Figures.

O autorze

The first part of this book is an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus on issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory.