Chaos in the core-periphery model

Currie, Martin; Kubin, Ingrid

doi:10.1016/j.jebo.2004.05.006

Cited by 24 publications

(22 citation statements)

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“…We consider the slightly different assumptions of Fujita et al (1999) as used in the discrete version proposed by Currie & Kubin (2006). Below is a very short description of the model which should suffice for readers familiar with the literature.…”

Section: The Core-periphery Model: a Brief Descriptionmentioning

confidence: 99%

“…To the best of our knowledge, Currie & Kubin (2006) 1 provide the first discretetime version of the core-periphery model. The dramatic appearance of chaos in this model explains, perhaps, the fact that no developments by other authors succeeded this first attempt at discretisation.…”

Section: Introductionmentioning

confidence: 99%

“…There are, however, further developments of this discrete-time framework, all of which bring cautionary remarks concerning unpredictability and chaos: see Commendatore et al (2008) for a description of catastrophic effects of 'minute changes in a tax or a subsidy', as well as the extension to three regions by Commendatore & Kubin (2013). In Currie & Kubin (2006), the effects of chaotic dynamics are so extreme that workers are seen to settle in the region providing the lowest utility, thus contradicting the assumptions of the model.…”

Section: Introductionmentioning

confidence: 99%

“…We provide references for those readers requiring more detail. Section 3 looks at the Dynamics for the Core-periphery Model 37 sources and consequences of chaos in the model of Currie & Kubin (2006). In Section 4, a new model is proposed and analysed.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Dynamics for the Core-periphery Model

Garrido-da-Silva¹,

Castro²,

Vasconcelos³

2015

Spatial Economic Analysis

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It is known that the discretisation of continuous-time models can introduce chaotic behaviour, even when this is not consistent with observations or even the model's assumptions. We propose generic dynamics describing discrete-time core-periphery models that comply with the established assumptions in the literature and are consistent with observed behaviour. The desired properties of the dynamics are proved analytically in the general case. We also give particular forms for the dynamics for those interested in applying our model.Dynamique discrète pour le modèle centre-périphérie RÉSUMÉ On sait que la discrétisation de modèles en temps continu peut introduire un comportement chaotique, même lorsque ceci est en contradiction avec les observations, voire des hypothèses du modèle. Nous proposons une dynamique générique décrivant des modèles centre-périphérie en temps discret, conformes aux hypothèses reconnues dans la littérature, et correspondant au comportement relevé. Les propriétés désirées de la dynamique sont prouvées de façon analytique dans un cas général. Nous fournissons également, pour ceux qui souhaiteraient appliquer notre modèle, des formes particulières pour la dynamique.Dinámica discreta del modelo de periferia central RESUMEN Se sabe que la discretización de los modelos de tiempo continuo pueden generar comportamientos caóticos, incluso en los casos en que esto no es coherente con las observaciones o las suposiciones del modelo. Proponemos una dinámica discreta que describe los modelos de periferia central de tiempo discreto que cumplen con las suposiciones establecidas en la literatura y son coherentes con el comportamiento observado. Las propiedades deseadas de la dinámica se comprueban de manera analítica en el caso general. También damos formularios especiales para la dinámica para aquellos que estén interesados en utilizar nuestro modelo.

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Section: The Core-periphery Model: a Brief Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete Dynamics for the Core-periphery Model

Garrido-da-Silva¹,

Castro²,

Vasconcelos³

2015

Spatial Economic Analysis

View full text Add to dashboard Cite

show abstract

“…3 See for an exploration of the Footloose Capital Model without taxation; and Currie and Kubin (2006) for a more general exploration of the implications of specifying models of the new Economic Geography in discrete time.…”

Section: Introductionmentioning

confidence: 99%

Source Versus Residence: A Comparison from a New Economic Geography Perspective

Kubin

Commendatore

2008

SSRN Journal

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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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Chaos in the core-periphery model

Cited by 24 publications

References 11 publications

Discrete Dynamics for the Core-periphery Model

Discrete Dynamics for the Core-periphery Model

Source Versus Residence: A Comparison from a New Economic Geography Perspective

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

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