Active stabilization of a chaotic urban system

Haag, Günter; Hagel, Tilo; Sigg, T.

doi:10.1155/s1026022697000137

Cited by 5 publications

(2 citation statements)

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“…Ya hemos dicho que originalmente el modelo pretendía describir la dinámica atmosférica y que Haken extendió su aplicación al caso de cierto tipo de láseres; sin embargo, hay más: diversos modelos de sistemas mecánicos [12][13][14][15], hidrodinámicos [16][17][18] o incluso económicos [19][20][21] son isomorfos a las ecuaciones de Lorenz. También son numerosas las observaciones experimentales, como las de Weiss en láseres [22,23] u otras como las de Illing en norias de agua [24].…”

Section: C Versatilidad Del Modelo De Lorenzunclassified

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

García-Ferrer¹,

Roldán²,

Silva³

et al. 2017

Opt. Pura Apl.

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ABSTRACT:We describe a practice designed for the numerical study of the Lorenz model that is a central model in the physics of lasers. The didactical objectives pursued in this practice have a dual nature, considering both the introduction to the knowledge of a physical paradigm of deterministic chaos as the training for the use of certain computational tools for its characterization. The method used to achieve programming is finding solutions of the Lorenz model and systematically studying of their temporal evolution using a Mathematica program. In the academic context, the practice is designed to be included in the curriculum of the degree in physics and to facilitate adaptation to other matters in this area, such as quantum optics, fluids, mechanical vibrations, etc. We first study the steady states, and their linear stability, of the Lorenz model equations and then numerically study the different types of dynamic behavior. We pay special attention to the deterministic chaotic behavior and to the sequence of bifurcations leading from periodic to chaotic behavior (routes to chaos).Key words: Lorenz model, chaos, nonlinear dynamics, laser, didactic, Mathematica. RESUMEN:Describimos una práctica diseñada para el estudio numérico de un modelo central en la física del láser, el modelo de Lorenz. Los objetivos didácticos que se persiguen en la práctica tienen una naturaleza doble, por un parte, la introducción al conocimiento de un paradigma físico del caos determinista y, por otra, la capacitación para la utilización de ciertas herramientas computacionales que permiten su caracterización. El método utilizado para alcanzarlos es la búsqueda de las soluciones del modelo de Lorenz y el estudio sistemático de su evolución temporal mediante el programa Mathematica. En el contexto académico, la práctica está diseñada para ser incluida en el currículum del grado en Física y para facilitar su adaptación a otras materias dentro de este ámbito, como puede ser óptica cuántica, fluidos, oscilaciones mecánicas, etc. Partiendo de las ecuaciones del modelo de Lorenz, estudiamos sus estados estacionarios y su estabilidad lineal, para después estudiar numéricamente los distintos tipos de comportamiento dinámico. Prestamos especial atención al comportamiento caótico determinista y a la secuencia de bifurcaciones que lleva de los comportamientos periódicos a los caóticos (rutas al caos).Palabras clave: Modelo de Lorenz, caos, dinámica no lineal, láser, didáctica, Mathematica. REFERENCES AND LINKS / REFERENCIAS Y ENLACES[1] E.N. Lorenz, "Deterministic nonperiodic flow", J. Atm. Sci. 20, 130-141 (1963).

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Section: C Versatilidad Del Modelo De Lorenzunclassified

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

García-Ferrer¹,

Roldán²,

Silva³

et al. 2017

Opt. Pura Apl.

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“…Holyst, Hagel, Haag, and Weidlich (1996) apply the OGY method to a case of two competing firms with asymmetric investment strategies and Haag, Hagel, and Sigg (1997) apply the OGY method to stabilizing a chaotic urban system, while Kopel (1997) applies the global targeting method to a model of disequilibrium dynamics with financial feedbacks as do Bala, Majumdar, and Mitra (1998) to a model of tâtonnement adjustment. Kaas (1998) suggests the application of both in a macroeconomic stabilization context.…”

Section: Controlling Chaosmentioning

confidence: 99%

Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems

Rosser

2011

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except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) PrefaceThis is, therefore, the intensest rendezvous. It is in that thought that we collect ourselves, Out of all the indifferences, into one thing:Within a single thing, a single shawl Wrapped tight round us, since we are poor, a warmth, A light, a power, the miraculous influence.Here now, we forget each other and ourselves. We feel the obscurity of an order, a whole. . . Wallace Stevens, 1950, Final Soliloquy of the Interior ParamourWithin the past decade we have seen on the one hand the majority of the world's population come to reside in urban areas for the first time in world history, while on the other we have seen a dramatic rise in average global temperature widely thought to be mostly due to the economic activities humans carry out in those urban areas. Nonlinear complex dynamics are profoundly involved in both of these related developments. This book will open with considering the historical forces behind this rise of cities, including some critiques of certain recent ideas of "new economic geography," and will conclude (except for a mathematical appendix) with a consideration of the science and economics of global warming and how to deal with it in the face of the uncertainties arising from these nonlinear complex dynamics, which will reflect the unique perspective of this author having been involved with climatological research for more than 35 years. In between there will be discussions of broader regional economic dynamics, the foundations of evolutionary theory, and the dynamics of ecologic-economic systems. A deep theme is that in all of these areas, nonlinear complex dynamics can result in discontinuities, such as sudden changes of urban growth patterns or the sudden crashes of biological populations harvested by human beings. These discontinuities can appear with little warning and can serve as the basis for the theories of unexpected events such as "black swans" as proposed by Nassim Taleb (2010).

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Economic Models with Exogenous Continuous/Discrete Shocks

Akhmet

Fen

2015

Nonlinear Physical Science

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Active stabilization of a chaotic urban system

Cited by 5 publications

References 12 publications

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems

Economic Models with Exogenous Continuous/Discrete Shocks

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