Differential Equations, Bifurcations, and Chaos in Economics

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World Scientific, 2005 - Business & Economics - 489 pages
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Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.
 

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Contents

Differential Equations in Economics
1
Scalar Linear Differential Equations
16
Scalar Nonlinear Differential Equations
53
Economic Dynamics with Scalar Differential Equations
92
Planar Linear Differential Equations
156
Planar Nonlinear Differential Equations
182
Planar Dynamical Economical Systems
241
HigherDimensional Differential Equations
304
HigherDimensional Nonlinear Differential Equations
329
HigherDimensional Economic Evolution
382
Economic Evolution with Changeable Speeds and Structures
446
Appendix
455
Bibliography
475
Index
483
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