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Estudio De La Estabilidad Y De Las Bifurcaciones De Los Equilibrios De Un Sistema Dinámico. Aplicación Al Mercado Cervecero Español/Stability and bifurcations in a dynamical model of current and potential market. An application to the Spanish beer market

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Author Info

  • VELASCO MORENTE, F.

    ()
    (Grupo COSDE. Universidad de Sevilla. Dpto. Economía Aplicada I. Avda. Ramón y Cajal, 1. 41018 Sevilla.)

  • NADAL MORALES, P.

    ()
    (Grupo COSDE. Universidad de Sevilla. Dpto. Economía Aplicada I. Avda. Ramón y Cajal, 1. 41018 Sevilla.)

  • GONZÁLEZ ABRIL, L.

    ()
    (Grupo COSDE. Universidad de Sevilla. Dpto. Economía Aplicada I. Avda. Ramón y Cajal, 1. 41018 Sevilla.)

  • VÍLCHEZ LOBATO, M. L.

    ()
    (Universidad de Huelva. Dpto. de Economía General y Estadística. Plaza de la Merced, 11. 21071 Huelva.)

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    Abstract

    En este trabajo estudiamos la existencia de bifurcaciones de codimensión uno en un modelo dinámico económico, en tiempo discreto, que relaciona el mercado actual y potencial de una colectividad cualquiera. En primer lugar, se establecen condiciones necesarias y sufi cientes para la estabilidad del único equilibrio del sistema, en función de los parámetros económicos del modelo. Esto nos permite la clasifi cación de dicho equilibrio en el espacio paramétrico. En este contexto, la estabilidad estructural es un punto clave a estudiar, esto es, si las propiedades dinámicas cualitativas del sistema persisten bajo pequeñas perturbaciones en su estructura. Este es el primer paso en el análisis de bifurcaciones. Los valores de los parámetros para los cuales el sistema no es estructuralmente estable, reciben el nombre de valores de bifurcación. Es por ello que en segundo lugar se analizan los cambios en el número y/o la estabilidad de los equilibrios del sistema, conforme a variaciones en los parámetros del mismo, centrando la atención en las bifurcaciones de codimensión 1 (Flip, Fold y Neimark-Sacker). Finalmente, se estudia el caso del mercado cervecero español, considerando como referencia la marca San Miguel. Se analiza su evolución y se da la interpretación económica de los resultados obtenidos. This paper deals with the theory of codimension one bifurcations applied to a discrete-time economic dynamic model, that relates the current and potential market of a collective anyone. First, some necessary and suffi cient conditions are established for the stability of the only stationary state of the system, according to the values of the economic parameters of the model. This allow us to classify the equilibrium point in a parametric space. In this context, structural stability is a key point to study, that is, if the qualitative dynamic properties of the system persist when its structure is perturbed. The study of the structural stability is the fi rst step to follow in the analysis of the bifurcations lying in the system. The values of the parameters for which the system is not structurally stable are called bifurcation values. So secondly, changes in the number and/or the stability of stationay states are analyzed, focussing our attention on codimension one bifurcations (Flip, Fold and Neimark-Sacker bifurcations). Finally, a numerical example is presented where results are applied to the Spanish beer market. A time evolution analysis is made and we give economic sense to the obtained results.

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    Bibliographic Info

    Article provided by Estudios de Economía Aplicada in its journal Estudios de Economía Aplicada.

    Volume (Year): 25 (2007)
    Issue (Month): (Abril)
    Pages: 419-452

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    Handle: RePEc:lrk:eeaart:25_1_16

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    Keywords: Estabilidad; Bifurcación de codimensión 1; Mercado cervecero español/Stability; Codimension one bifurcation; Spanish brewer market.;

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