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Author: Hans-Walter Lorenz
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Author: Hans-Walter Lorenz
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 344
Get Book Here
Book Description
Author: Thierry Vialar
Publisher: Springer Science & Business Media
ISBN: 3540859780
Category : Business & Economics
Languages : en
Pages : 752
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Book Description
Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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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.
Author: William A. Barnett
Publisher: Cambridge University Press
ISBN: 9780521471411
Category : Business & Economics
Languages : en
Pages : 426
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Book Description
This 1997 book presents developments in nonlinear economic dynamics along with related research from other fields, including mathematics, statistics, biology, and physics.
Author: Marji Lines
Publisher: Springer Science & Business Media
ISBN: 3211380434
Category : Business & Economics
Languages : en
Pages : 238
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Book Description
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.
Author: Franco Gori
Publisher: Springer Science & Business Media
ISBN: 3642580319
Category : Business & Economics
Languages : en
Pages : 371
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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.
Author: Moshe Gitterman
Publisher: World Scientific
ISBN: 9814464244
Category : Science
Languages : en
Pages : 157
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Book Description
Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics.
Author: Wei-bin Zhang
Publisher: World Scientific
ISBN: 981126743X
Category : Mathematics
Languages : en
Pages : 228
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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.
Author: Abraham C.-L. Chian
Publisher: Springer Science & Business Media
ISBN: 3540397523
Category : Business & Economics
Languages : en
Pages : 109
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Book Description
Economic Systems exhibit complex dynamics evidenced by large-amplitude and aperiodic fluctuations in economic variables, such as foreign exchange rates and stock market prices, indicating that these systems are driven far from the equilibrium. Characterization of the complex behavior of economic cycles, by identifying regular and irregular patterns and regime switching in economic time series, is the key for pattern recognition and forecasting of economic cycles. Statistical analysis of stock markets and foreign exchange markets has demonstrated the intermittent nature of economic time series. A nonlinear model of business cycles is able to simulate intermittency arising from order-chaos and chaos-chaos transitions. This monograph introduces new concepts of unstable periodic orbits and chaotic saddles which are unstable structures embedded in a chaotic attractor, responsible for economic intermittency.
Author: J. Barkley Rosser
Publisher: Springer Science & Business Media
ISBN: 9401716137
Category : Business & Economics
Languages : en
Pages : 313
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Book Description
From Catastrophe to Chaos: A General Theory of Economic Discontinuities presents and unusual perspective on economics and economic analysis. Current economic theory largely depends upon assuming that the world is fundamentally continuous. However, an increasing amount of economic research has been done using approaches that allow for discontinuities such as catastrophe theory, chaos theory, synergetics, and fractal geometry. The spread of such approaches across a variety of disciplines of thought has constituted a virtual intellectual revolution in recent years. This book reviews the applications of these approaches in various subdisciplines of economics and draws upon past economic thinkers to develop an integrated view of economics as a whole from the perspective of inherent discontinuity.
