Nonlinear Dynamics In Equilibrium Models

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Nonlinear Dynamics in Equilibrium Models

John Stachurski,Alain Venditti,Makoto Yano
Nonlinear Dynamics in Equilibrium Models Book PDF

Author : John Stachurski,Alain Venditti,Makoto Yano
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 44,7 Mb
Release : 2012-01-25
Category : Business & Economics
ISBN : 9783642223976

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Nonlinear Dynamics in Equilibrium Models by John Stachurski,Alain Venditti,Makoto Yano Pdf

Optimal growth theory studies the problem of efficient resource allocation over time, a fundamental concern of economic research. Since the 1970s, the techniques of nonlinear dynamical systems have become a vital tool in optimal growth theory, illuminating dynamics and demonstrating the possibility of endogenous economic fluctuations. Kazuo Nishimura's seminal contributions on business cycles, chaotic equilibria and indeterminacy have been central to this development, transforming our understanding of economic growth, cycles, and the relationship between them. The subjects of Kazuo's analysis remain of fundamental importance to modern economic theory. This book collects his major contributions in a single volume. Kazuo Nishimura has been recognized for his contributions to economic theory on many occasions, being elected fellow of the Econometric Society and serving as an editor of several major journals. Chapter “Introduction” is available open access under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License via link.springer.com.

Price Dynamics in Equilibrium Models

Jan Tuinstra
Price Dynamics in Equilibrium Models Book PDF

Author : Jan Tuinstra
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461516613

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Price Dynamics in Equilibrium Models by Jan Tuinstra Pdf

A long-standing unsolved problem in economic theory is how economic equilibria are attained. Price Dynamics in Equilibrium Models: The Search for Equilibrium and the Emergence of Endogenous Fluctuations considers a number of adjustment processes in different economic models and investigates their dynamical behaviour. Two important themes arising in this context are `bounded rationality' and `nonlinear dynamics'. Important sub-themes of the book are the following: how do boundedly rational agents interact with their environment and does this interaction in some sense lead to rational outcomes (which may or may not correspond to equilibria)? The second sub-theme deals with the consequences of the nonlinear dynamical nature of many adjustment processes. The results presented in this volume indicate that endogenous fluctuations are the rule rather than the exception in the search for equilibrium. The book uses the theory of nonlinear dynamics to analyze the dynamics of the different economic models. Due to the complexity of most of the models, an important role is played by computational methods. In particular, at regular instances the models are analyzed by numerical simulations and some computer-assisted proofs are provided. It also covers a wide range of dynamical models from economic theory. Most of these models merge the theory of nonlinear economic dynamics with the theory of bounded rationality. The book is written for anyone with an interest in economic theory in general and bounded rationality and endogenous fluctuations in particular. It is entirely self-contained and accessible to readers with only a limited knowledge of economic theory.

Applications of Nonlinear Dynamics

Visarath In,Patrick Longhini,Antonio Palacios
Applications of Nonlinear Dynamics Book PDF

Author : Visarath In,Patrick Longhini,Antonio Palacios
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 50,6 Mb
Release : 2009-02-11
Category : Technology & Engineering
ISBN : 9783540856320

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Applications of Nonlinear Dynamics by Visarath In,Patrick Longhini,Antonio Palacios Pdf

The ?eld of applied nonlinear dynamics has attracted scientists and engineers across many different disciplines to develop innovative ideas and methods to study c- plex behavior exhibited by relatively simple systems. Examples include: population dynamics, ?uidization processes, applied optics, stochastic resonance, ?ocking and ?ightformations,lasers,andmechanicalandelectricaloscillators. Acommontheme among these and many other examples is the underlying universal laws of nonl- ear science that govern the behavior, in space and time, of a given system. These laws are universal in the sense that they transcend the model-speci?c features of a system and so they can be readily applied to explain and predict the behavior of a wide ranging phenomena, natural and arti?cial ones. Thus the emphasis in the past decades has been in explaining nonlinear phenomena with signi?cantly less att- tion paid to exploiting the rich behavior of nonlinear systems to design and fabricate new devices that can operate more ef?ciently. Recently, there has been a series of meetings on topics such as Experimental Chaos, Neural Coding, and Stochastic Resonance, which have brought together many researchers in the ?eld of nonlinear dynamics to discuss, mainly, theoretical ideas that may have the potential for further implementation. In contrast, the goal of the 2007 ICAND (International Conference on Applied Nonlinear Dynamics) was focused more sharply on the implementation of theoretical ideas into actual - vices and systems.

From Instability to Intelligence

Michail Zak,Joseph P. Zbilut,Ronald E. Meyers
From Instability to Intelligence Book PDF

Author : Michail Zak,Joseph P. Zbilut,Ronald E. Meyers
Publisher : Springer Science & Business Media
Page : 559 pages
File Size : 44,8 Mb
Release : 2008-12-11
Category : Science
ISBN : 9783540691211

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From Instability to Intelligence by Michail Zak,Joseph P. Zbilut,Ronald E. Meyers Pdf

So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.

Nonlinear Dynamical Systems in Economics

Marji Lines
Nonlinear Dynamical Systems in Economics Book PDF

Author : Marji Lines
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 40,9 Mb
Release : 2007-03-23
Category : Business & Economics
ISBN : 9783211380437

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Nonlinear Dynamical Systems in Economics by Marji Lines Pdf

Many problems in theoretical economics are mathematically formalized as dynam ical systems of difference and differential equations. In recent years a truly open approach to studying the dynamical behavior of these models has begun to make its way into the mainstream. That is, economists formulate their hypotheses and study the dynamics of the resulting models rather than formulating the dynamics and studying hypotheses that could lead to models with such dynamics. This is a great progress over using linear models, or using nonlinear models with a linear approach, or even squeezing economic models into well-studied nonlinear systems from other fields. There are today a number of economic journals open to publishing this type of work and some of these have become important. There are several societies which have annual meetings on the subject and participation at these has been growing at a good rate. And of course there are methods and techniques avail able to a more general audience, as well as a greater availability of software for numerical and graphical analysis that makes this type of research even more excit ing. The lecturers for the Advanced School on Nonlinear Dynamical Systems in Economics, who represent a wide selection of the research areas to which the the ory has been applied, agree on the importance of simulations and computer-based analysis. The School emphasized computer applications of models and methods, and all contributors ran computer lab sessions.

Nonlinear Economic Dynamics

Tönu Puu
Nonlinear Economic Dynamics Book PDF

Author : Tönu Puu
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642972911

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Nonlinear Economic Dynamics by Tönu Puu Pdf

The present study is a preliminary draft on nonlinear economic dynamics, with which the author has been concerned the last years. It grew out from the joint work by Professor Martin Beckmann and the present author on nonlinear statics in spatial economics, Beckmann and Puu, "Spatial Economics" (North-Holland 1985). The monograph mentioned contains sections on price waves and business cycles, but in a linear format. The rest is static theory. The author has finally come to the conviction that linear dynamic modelling has very little to yield. This is due to the poor set of alternatives -decay or explosion of motion -pertinent to linear models. Therefore, the present work centres on non-linearity. Another distinction is that only purely causal models are dealt with, as those formatted as inter-temporal equilibria hardly belong to the more restricted field of dynamics. The spatial origin is visible in the choice of models. Chapter 2 summarizes the work by the author on the structural stability of continuous spatial market equilibrium models. Chapter 3 deals with a re-fonnulation of the ingenious population growth and diffusion model invented by the young Hotelling in 1921. Chapter 4 is a detailed digression on business cycle models in a continuous spatial format with inter-regional trade.

Nonlinear Dynamics in Economics

Bärbel Finkenstädt
Nonlinear Dynamics in Economics Book PDF

Author : Bärbel Finkenstädt
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642468216

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Nonlinear Dynamics in Economics by Bärbel Finkenstädt Pdf

1. 1 Introduction In economics, one often observes time series that exhibit different patterns of qualitative behavior, both regular and irregular, symmetric and asymmetric. There exist two different perspectives to explain this kind of behavior within the framework of a dynamical model. The traditional belief is that the time evolution of the series can be explained by a linear dynamic model that is exogenously disturbed by a stochastic process. In that case, the observed irregular behavior is explained by the influence of external random shocks which do not necessarily have an economic reason. A more recent theory has evolved in economics that attributes the patterns of change in economic time series to an underlying nonlinear structure, which means that fluctua tions can as well be caused endogenously by the influence of market forces, preference relations, or technological progress. One of the main reasons why nonlinear dynamic models are so interesting to economists is that they are able to produce a great variety of possible dynamic outcomes - from regular predictable behavior to the most complex irregular behavior - rich enough to meet the economists' objectives of modeling. The traditional linear models can only capture a limited number of possi ble dynamic phenomena, which are basically convergence to an equilibrium point, steady oscillations, and unbounded divergence. In any case, for a lin ear system one can write down exactly the solutions to a set of differential or difference equations and classify them.

Nonlinear Dynamics New Directions

Hernán González-Aguilar,Edgardo Ugalde
Nonlinear Dynamics New Directions Book PDF

Author : Hernán González-Aguilar,Edgardo Ugalde
Publisher : Springer
Page : 240 pages
File Size : 40,5 Mb
Release : 2015-02-10
Category : Technology & Engineering
ISBN : 9783319098647

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Nonlinear Dynamics New Directions by Hernán González-Aguilar,Edgardo Ugalde Pdf

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynamics in biological · Includes a study of self-organized regularity in long-range systems · Explains use of Levenstein's distance for measuring lexical evolution rates

Non-Linear Dynamics Near and Far from Equilibrium

J.K. Bhattacharjee,S. Bhattacharyya
Non Linear Dynamics Near and Far from Equilibrium Book PDF

Author : J.K. Bhattacharjee,S. Bhattacharyya
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 45,5 Mb
Release : 2007-12-27
Category : Science
ISBN : 9781402053887

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Non-Linear Dynamics Near and Far from Equilibrium by J.K. Bhattacharjee,S. Bhattacharyya Pdf

This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group, and self-consistent mode coupling.

Nonlinear Dynamics, Mathematical Biology, and Social Science

Joshua M. Epstein
Nonlinear Dynamics Mathematical Biology and Social Science Book PDF

Author : Joshua M. Epstein
Publisher : CRC Press
Page : 177 pages
File Size : 49,6 Mb
Release : 2018-03-08
Category : Mathematics
ISBN : 9780429961953

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Nonlinear Dynamics, Mathematical Biology, and Social Science by Joshua M. Epstein Pdf

This book is based on a series of lectures on mathematical biology, the essential dynamics of complex and crucially important social systems, and the unifying power of mathematics and nonlinear dynamical systems theory.

Perspectives of Nonlinear Dynamics: Volume 2

E. Atlee Jackson
Perspectives of Nonlinear Dynamics Volume 2 Book PDF

Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 676 pages
File Size : 42,6 Mb
Release : 1989
Category : Mathematics
ISBN : 0521426332

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Perspectives of Nonlinear Dynamics: Volume 2 by E. Atlee Jackson Pdf

The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.

New Trends in Nonlinear Dynamics and Control, and their Applications

Wei Kang,Mingqing Xiao,Carlos Borges
New Trends in Nonlinear Dynamics and Control and their Applications Book PDF

Author : Wei Kang,Mingqing Xiao,Carlos Borges
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 48,6 Mb
Release : 2003-09-16
Category : Technology & Engineering
ISBN : 3540404740

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New Trends in Nonlinear Dynamics and Control, and their Applications by Wei Kang,Mingqing Xiao,Carlos Borges Pdf

A selection of papers exploring a wide spectrum of new trends in nonlinear dynamics and control, such as bifurcation control, state estimation and reconstruction, analysis of behavior and stabilities, dynamics of nonlinear neural network models, and numerical algorithms. The papers focus on new ideas and the latest developments in both theoretical and applied research topics of nonlinear control. Because many of the authors are leading researchers in their own fields, the papers presented in this volume reflect the state of the art in the areas of nonlinear dynamics and control. Many of the papers in this volume were first presented at the highly succesful ''Symposium on New Trends in Nonlinear Dynamics and Control, and Their Applications,'' held October 18-19, 2002, in Monterey, California.

Perspectives of Nonlinear Dynamics: Volume 1

E. Atlee Jackson
Perspectives of Nonlinear Dynamics Volume 1 Book PDF

Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 532 pages
File Size : 42,5 Mb
Release : 1989
Category : Mathematics
ISBN : 0521426324

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Perspectives of Nonlinear Dynamics: Volume 1 by E. Atlee Jackson Pdf

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.

Nonlinear Dynamical Economics and Chaotic Motion

Hans-Walter Lorenz
Nonlinear Dynamical Economics and Chaotic Motion Book PDF

Author : Hans-Walter Lorenz
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642783241

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Nonlinear Dynamical Economics and Chaotic Motion by Hans-Walter Lorenz Pdf

Usually, the first edition of a book still contains a multiplicity of typographic, con ceptional, and computational errors even if one believes the opposite at the time of publication. As this book did not represent a counterexample to this rule, the current second edition offers a chance to remove at least the known shortcomings. The book has been partly re-organized. The previously rather long Chapter 4 has been split into two separate chapters dealing with discrete-time and continuous time approaches to nonlinear economic dynamics. The short summary of basic properties of linear dynamical systems has been banned to an appendix because the line of thought in the chapter seems to have been unnecessarily interrupted by these technical details and because the book concentrates on nonlinear systems. This appendix, which mainly deals with special formal properties of dynamical sys tems, also contains some new material on invariant subspaces and center-manifold reductions. A brief introduction into the theory of lags and operators is followed by a few remarks on the relation between the 'true' properties of dynamical systems and their behavior observable in numerical experiments. Additional changes in the main part of the book include a re-consideration of Popper's determinism vs. inde terminism discussion in the light of chaotic properties of deterministic, nonlinear systems in Chapter 1. An investigation of a simultaneous price-quantity adjustment process, a more detailed inquiry into the uniqueness property of limit cycles, and a short presentation of relaxation oscillations are included in Chapter 2.

Mathematical Modeling and Applications in Nonlinear Dynamics

Albert C.J. Luo,Hüseyin Merdan
Mathematical Modeling and Applications in Nonlinear Dynamics Book PDF

Author : Albert C.J. Luo,Hüseyin Merdan
Publisher : Springer
Page : 205 pages
File Size : 53,7 Mb
Release : 2016-01-28
Category : Technology & Engineering
ISBN : 9783319266305

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Mathematical Modeling and Applications in Nonlinear Dynamics by Albert C.J. Luo,Hüseyin Merdan Pdf

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.