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Differential Equations, Bifurcations, and Chaos in Economics

Author : Wei-Bin Zhang

Publisher : World Scientific

Page : 512 pages

File Size : 24,70 MB

Release : 2005

Category : Business & Economics

ISBN : 9812563334

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Book Description

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.



Differential Equations, Bifurcations And Chaos In Economics

Author : Wei-bin Zhang

Publisher : World Scientific Publishing Company

Page : 510 pages

File Size : 44,85 MB

Release : 2005-07-18

Category : Business & Economics

ISBN : 9813106514

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Book Description

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.



Attractors, Bifurcations, & Chaos

Author : Tönu Puu

Publisher : Springer Science & Business Media

Page : 572 pages

File Size : 14,48 MB

Release : 2003-07-10

Category : Mathematics

ISBN : 9783540402268

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Book Description

Attractors, Bifurcations, & Chaos - now in its second edition - begins with 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.



Mathematical Models in Economics - Volume I

Author : Wei-Bin Zhang

Publisher : EOLSS Publications

Page : 542 pages

File Size : 49,57 MB

Release : 2009-06-10

Category : Economics

ISBN : 1848262280

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Book Description

Mathematical Models in Economics is a component of Encyclopedia of Mathematical Sciences in which is part of the global Encyclopedia of Life Support Systems (EOLSS), an integrated compendium of twenty one Encyclopedias. This theme is organized into several different topics and introduces the applications of mathematics to economics. Mathematical economics has experienced rapid growth, generating many new academic fields associated with the development of mathematical theory and computer. Mathematics is the backbone of modern economics. It plays a basic role in creating ideas, constructing new theories, and empirically testing ideas and theories. Mathematics is now an integral part of economics. The main advances in modern economics are characterized by applying mathematics to various economic problems. Many of today's profound insights into economic problems could hardly be obtained without the help of mathematics. The concepts of equilibrium versus non-equilibrium, stability versus instability, and steady states versus chaos in the contemporary literature are difficult to explain without mathematics. The theme discusses on modern versions of some classical economic theories, taking account of balancing between significance of economic issues and mathematical techniques. These two volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.



Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz

Publisher : CRC Press

Page : 532 pages

File Size : 32,63 MB

Release : 2018-05-04

Category : Mathematics

ISBN : 0429961111

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Book Description

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.



Chaos, Complexity, And Nonlinear Economic Theory

Author : Wei-bin Zhang

Publisher : World Scientific

Page : 228 pages

File Size : 16,65 MB

Release : 2023-05-17

Category : Mathematics

ISBN : 981126743X

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Book Description

What do economic chaos and uncertainties mean in rational or irrational economic theories? How do simple deterministic interactions among a few variables lead to unpredictable complex phenomena? Why is complexity of economies causing so many conflicts and confusions worldwide?This book provides a comprehensive introduction to recent developments of complexity theory in economics. It presents different models based on well-accepted economic mechanisms such as the Solow model, Ramsey model, and Lucas model. It is focused on presenting complex behaviors, such as business cycles, aperiodic motion, bifurcations, catastrophes, chaos, and hidden attractors, in basic economic models with nonlinear behavior. It shows how complex nonlinear phenomena are identified from various economic mechanisms and theories. These models demonstrate that the traditional or dominant economic views on evolution of, for instance, capitalism market, free competition, or Keynesian economics, are not generally valid. Markets are unpredictable and nobody knows with certainty the consequences of policies or other external factors in economic systems with simple interactions.



Bifurcation Theory of Functional Differential Equations

Author : Shangjiang Guo

Publisher : Springer Science & Business Media

Page : 295 pages

File Size : 28,42 MB

Release : 2013-07-30

Category : Mathematics

ISBN : 1461469929

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Book Description

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).



Nonlinear Dynamics in Economics and Social Sciences

Author : Franco Gori

Publisher : Springer Science & Business Media

Page : 371 pages

File Size : 11,83 MB

Release : 2012-12-06

Category : Business & Economics

ISBN : 3642580319

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Book Description

This volume constitutes the Proceedings of the "Nonlinear Dynamics in Economics and Social Sciences" Meeting held at the Certosa di Pontignano, Siena, on May 27-30, 1991. The Meeting was organized by the National Group "Modelli Nonlineari in Economia e Dinamiche Complesse" of the Italian Ministery of University and SCientific Research, M.U.RS.T. The aim of the Conference, which followed a previous analogous initiative taking place in the very same Certosa, on January 1988*, was the one of offering a come together opportunity to economists interested in a new mathematical approach to the modelling of economical processes, through the use of more advanced analytical techniques, and mathematicians acting in the field of global dynamical systems theory and applications. A basiC underlying idea drove the organizers: the necessity of fOCUSing on the use that recent methods and results, as those commonly referred to the overpopularized label of "Chaotic Dynamics", did find in the social sciences domain; and thus to check their actual relevance in the research program of modelling economic phenomena, in order to individuate and stress promising perspectives, as well as to curb excessive hopes and criticize not infrequent cases where research reduces to mechanical, ad hoc, applications of "a la mode" techniques. In a word we felt the need of looking about the state of the arts in non-linear systems theory applications to economics and social processes: hence the title of the workshop and the volume.



Economic Growth Theory

Author : Wei-Bin Zhang

Publisher : Taylor & Francis

Page : 483 pages

File Size : 13,82 MB

Release : 2018-01-18

Category : Business & Economics

ISBN : 1351159437

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Book Description

This book develops a new theoretical framework to examine the issues of economic growth and development. Providing analysis of economic dynamics in a competitive economy under government intervention in infrastructure and income distribution, the book develops a unique analytical framework under the influence of traditional neoclassical growth theory. However, in a departure from neoclassical growth theory it examines both the Solow-Swan and the Ramsey growth models, introducing a utility function which treats consumer choices in ways critically different to previous approaches. Using practical examples and models the book demonstrates how this new direction can effectively analyze the key issues of economic growth, in a compact and comprehensive manner.



Introduction to Complexity and Complex Systems

Author : Robert B. Northrop

Publisher : CRC Press

Page : 554 pages

File Size : 12,22 MB

Release : 2010-12-08

Category : Medical

ISBN : 1439839018

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Book Description

The boundaries between simple and complicated, and complicated and complex system designations are fuzzy and debatable, even using quantitative measures of complexity. However, if you are a biomedical engineer, a biologist, physiologist, economist, politician, stock market speculator, or politician, you have encountered complex systems. Furthermore, your success depends on your ability to successfully interact with and manage a variety of complex systems. In order not to be blindsided by unexpected results, we need a systematic, comprehensive way of analyzing, modeling, and simulating complex systems to predict non-anticipated outcomes. In its engaging first chapters, the book introduces complex systems, Campbell's Law, and the Law of Unintended Consequences, and mathematics necessary for conversations in complex systems. Subsequent chapters illustrate concepts via commonly studied biological mechanisms. The final chapters focus on higher-level complexity problems, and introduce complexity in economic systems. Designed as a reference for biologists and biological engineers, Introduction to Complexity and Complex Systems lends itself to use in a classroom course to introduce advanced students studying biomedical engineering, biophysics, or physiology to complex systems. Engaging and illustrative, this book aids scientists and decision makers in managing biological complexity and complex systems.