Attractors, Bifurcations, & Chaos

1. Front Matter

   Pages I-XII

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2. Introduction

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   Pages 1-12

3. Differential Equations: Ordinary

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   Pages 13-94

4. Differential Equations: Partial

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   Pages 95-159

5. Iterated Maps or Difference Equations

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   Pages 161-216

6. Bifurcation and Catastrophe

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   Pages 217-238

7. Monopoly

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   Pages 239-260

8. Duopoly and Oligopoly

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   Pages 261-306

9. Business Cycles: Continuous Time

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   Pages 307-356

10. Business Cycles: Continuous Space

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    Pages 357-380

11. Business Cycles: Discrete Time

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    Pages 381-441

12. Dynamics of Interregional Trade

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    Pages 443-469

13. Development: Increasing Complexity

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    Pages 471-502

14. Development: Multiple Attractors

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    Pages 503-527

15. Back Matter

    Pages 529-549

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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.

• Chaos
• bifurcation
• business cycle
• differential equation
• dynamics
• economic dynamics
• economics
• equation
• nonlinear dynamics
• nonlinear systems
• nonlinearity
• regional science

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)

• Centre for Regional Science, Umeå University, Umeå, Sweden

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