Discrete dynamical systems, bifurcations and chaos in economics by Wei-Bin Zhang

Cover of: Discrete dynamical systems, bifurcations and chaos in economics | Wei-Bin Zhang

Published by Elsevier in Amsterdam, Boston .

Written in English

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Subjects:

  • Economics, Mathematical,
  • Difference equations,
  • Differentiable dynamical systems

About the Edition

This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics.

Key Features:

A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics. Mathematical definitions and theorems are introduced in a systematic and easily accessible way. Examples are from almost all fields of economics; technically proceeding from basic to advanced topics. Lively illustrations with numerous figures. Numerous simulation to see paths of economic dynamics. Comprehensive treatment of the subject with a comprehensive and easily accessible approach. Key Features:

A unique book concentrated on theory of discrete dynamical systems and its traditional as well as advanced applications to economics. Mathematical definitions and theorems are introduced in a systematic and easily accessible way. Examples are from almost all fields of economics; technically proceeding from basic to advanced topics. Lively illustrations with numerous figures. Numerous simulation to see paths of economic dynamics. Comprehensive treatment of the subject with a comprehensive and easily accessible approach.

Edition Notes

Book details

StatementWei-Bin Zhang.
SeriesMathematics in science and engineering -- v. 204
ContributionsScienceDirect (Online service)
Classifications
LC ClassificationsHB135 .Z537 2006
The Physical Object
Paginationix, 448 p. :
Number of Pages448
ID Numbers
Open LibraryOL18587262M
ISBN 100444521976
ISBN 109780444521972
LC Control Number2007310422

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This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability.

The purpose of the present chapter is once again to show on concrete new examples that chaos in one-dimensional unimodal mappings, dynamical chaos in systems of ordinary differential equations, diffusion chaos in systems of the equations with partial derivatives and chaos in Hamiltonian and conservative systems are generated by cascades of bifurcations under universal bifurcation.

From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations.

Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Get this from a library. Discrete dynamical systems, bifurcations and chaos in economics. [Wei-Bin Zhang] -- This book is a unique blend of difference equations theory and its exciting applications to economics.

It deals with not only theory of linear (and linearized) difference equations, but also. This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential in order to understand the fascinating behavior of nonlinear discrete dynamical systems.

The theory is illuminated by several examples and exercises, many of them taken from population dynamical studies. Discrete Dynamical Systems, Bifurcations and Chaos in Economics. This book is a unique blend of difference equations theory and its exciting applications to economics.

It deals with not only theory of linear (and linearized) difference equations, but also. The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics.

The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. Difference equations in economics 2. Scalar linear difference equations 3. One-dimensional dynamical economic systems 4.

Time-dependent solutions of scalar systems 5. Economic bifurcations and chaos 6. Higher dimensional difference equations 7. Higher dimensional economic dynamics 8. EpiloguePrice: $ 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.

Sincehe has been teaching undergraduate and graduate courses on applied mathematics. His primary research interests include bifurcations and chaos. He has authored or coauthored more than journal and conference papers and 15 books. He is the Editor-in-Chief of the Annual Review of Chaos Theory, Bifurcations and Dynamical Systems Journal.

Chaos is introduced at theoutset and is then incorporated as an integral part of the theoryof discrete dynamical systems in one or more dimensions. Both phasespace and parameter space analysis are developed with ampleexercises, more than figures, and important practical examplessuch as the dynamics of atmospheric changes and neuralnetworks.

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() A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems. Physics Letters A() Chaos in homeostatically regulated neural systems.

Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation.

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Maps. A discrete-time, affine dynamical system has the form of a matrix difference equation: + = +, with A a matrix and b a vector. As in the continuous case, the change of coordinates x → x + (1 − A) –1 b removes the term b from the equation. In the new coordinate system, the origin is a fixed point of the map and the solutions are of the linear system A n x 0.

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Interaction of Hopf and period doubling bifurcations, as a so-called codimension two singularity, may give rise to rich bifurcation outcomes depending on the two-parameter unfolding at the bifurcat.

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Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincare Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of Hilbert's Sixteenth Problem.- Linear Discrete Dynamical Systems.- Nonlinear Discrete Dynamical.

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Goodson Dynamical Systems and Chaos: Spring CONTENTS Chapter 1. The Orbits of One-Dimensional Maps Iteration of functions and examples of dynamical systems Newton’s method and fixed points Graphical iteration Attractors and repellers.Introduction to Applied Nonlinear Dynamical Systems and Chaos: Edition 2 - Ebook written by Stephen Wiggins.

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