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78570

Published
**2006** by Elsevier in Amsterdam, Boston .

Written in English

Read online- Economics, Mathematical,
- Difference equations,
- Differentiable dynamical systems

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**

Statement | Wei-Bin Zhang. |

Series | Mathematics in science and engineering -- v. 204 |

Contributions | ScienceDirect (Online service) |

Classifications | |
---|---|

LC Classifications | HB135 .Z537 2006 |

The Physical Object | |

Pagination | ix, 448 p. : |

Number of Pages | 448 |

ID Numbers | |

Open Library | OL18587262M |

ISBN 10 | 0444521976 |

ISBN 10 | 9780444521972 |

LC Control Number | 2007310422 |

**Download Discrete dynamical systems, bifurcations and chaos in economics**

Discrete dynamical systems, bifurcations and chaos in economics | Zhang W.B. | download | B–OK. Download books for free. Find books. Discrete Dynamical Systems, Bifurcations and Chaos in Economics (Volume ) (Mathematics in Science and Engineering (Volume )) 1st Edition by Wei-Bin Zhang (Author) › Visit Amazon's Wei-Bin Zhang Page.

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Print Book & E-Book. ISBNDiscrete Dynamical Systems, Bifurcations and Chaos in Economics Wei-Bin Zhang (Eds.) This book is a unique blend of difference equations theory and its exciting applications to economics. Request PDF | Discrete Dynamical Systems, Bifurcations and Chaos in Economics, Volume (Mathematics in Science and Engineering) | This book is a unique blend of.

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Everyday low prices and free delivery on eligible orders. The dynamics of our dynamical systems is thus determined by iteratively applying F s * to the initial state. Fixed points s stab of F s * are regarded to be the “answers” which the system gives to s ∗, as it is common procedure in neural network that in general there may be more than just one such stable state for the state transition mapping F s * that is determined by.

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.

Get this from a library. 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.

Based on the author's book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

() 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.

•The book begins with basic deﬁnitions and examples. Chapter 1 introduces the concepts of state vectors and divides the dynamical world into the discrete and the continuous. We then explore many instances of dynamical systems in the real world—our examples are drawn from physics, biology, economics, and numerical mathematics.

Chaos: An Introduction to Dynamical Systems, was developed and class-tested by a distinguished team of authors at two universities through their teaching of courses based on the material. Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites.4/5(4).

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex.

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.

Predescu, M. [Review of the book Discrete Chaos with Applications in Science and Engineering, 2nd. ed.,Chapman & Hall/CRC, Taylor & Francis Group, ISBN ]. Journal of Difference Equations and Applications. Predescu, M. [Review of the book Discrete Dynamical Systems, Bifurcations and Chaos in Economics, 1st.

We consider several discrete dynamical systems for which some invariants can be found. Our study includes complex Möbius transformations as well as the third-order Lyness recurrence. DYNAMICS OF SOME RATIONAL DISCRETE DYNAMICAL SYSTEMS VIA INVARIANTS | International Journal of Bifurcation and Chaos.

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Print Book & E-Book. ISBNdynamical systems is discussed,namely,reaction-diﬀusion systems. gicalequivalence,bifurcations,andstructural stabilityofdynamicalsystems. Two dynamical systems are called topo-logicallyequivalentif their phase portraits are homeomorphic. This notion is 1Renamed in as the Institute of Mathematical Problems of Biology (IMPB).

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.

This introduction to dynamical systems theory treats both discrete dynamical systems and continuous systems. Driven by numerous examples from a broad range of disciplines and requiring only knowledge of ordinary differential equations, the text emphasizes applications and simulation utilizing MATLAB®, Simulink®, and the Symbolic Math toolbox.

Beginning with a tutorial guide to MATLAB®, the. stochastic. Chaos in Dynamical Systems, Edward Ott,Mathematics, pages. New edition of the best-selling graduate textbook on chaos for scientists and engineers.

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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.

Books • Nonlinear Dynamics and Chaos, by Steven H. Strogatz, Perseus Books Group, This book provides a very readable introduction to dynamical systems, with lots Dynamical Systems, and Bifurcations of Vector Fields Discrete time systems: maps Consider the ﬁrst-order diﬀerence system x n+1 = F(x n,n), () where x.LECTURE NOTES ON DYNAMICAL SYSTEMS, CHAOS AND FRACTAL GEOMETRY Geoﬀrey R.

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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