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Models of Continuous Dynamics on the 2-Simplex and Applications in Economics

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  • Stijepic, Denis

Abstract

In this paper, we discuss the models of continuous dynamics on the 2-simplex that arise when different qualitative restrictions are imposed on the (continuous) functions that generate the dynamics on the 2-simplex. We consider three types of qualitative restrictions: inequality (or set-theoretical) conditions, monotonicity/curvature (or differential-geometrical) conditions, and topological conditions (referring to (transversal) non-(self-)intersection of trajectories). We discuss the implications of these restrictions for transitional and limit dynamics on the 2-simplex and the wide range of potential and existing applications of the resulting system-theoretical models in economics and, in particular, in economic growth and development theory.

Suggested Citation

  • Stijepic, Denis, 2018. "Models of Continuous Dynamics on the 2-Simplex and Applications in Economics," MPRA Paper 86341, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:86341
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    References listed on IDEAS

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    1. Silva, Ester G. & Teixeira, Aurora A.C., 2008. "Surveying structural change: Seminal contributions and a bibliometric account," Structural Change and Economic Dynamics, Elsevier, vol. 19(4), pages 273-300, December.
    2. Denis Stijepic, 2017. "An argument against Cobb-Douglas production functions (in multi-sector growth modeling)," Economics Bulletin, AccessEcon, vol. 37(2), pages 1143-1150.
    3. Herrendorf, Berthold & Rogerson, Richard & Valentinyi, Ákos, 2014. "Growth and Structural Transformation," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 6, pages 855-941, Elsevier.
    4. Stijepic, Denis, 2017. "On development paths minimizing the structural change costs in the three-sector framework and an application to structural policy," MPRA Paper 77023, University Library of Munich, Germany, revised 22 Feb 2017.
    5. Stijepic, Denis, 2015. "A geometrical approach to structural change modelling," Structural Change and Economic Dynamics, Elsevier, vol. 33(C), pages 71-85.
    6. Schettkat, Ronald & Yocarini, Lara, 2006. "The shift to services employment: A review of the literature," Structural Change and Economic Dynamics, Elsevier, vol. 17(2), pages 127-147, June.
    7. Stijepic, Denis, 2017. "Empirical evidence on the geometrical properties of structural change trajectories," MPRA Paper 80854, University Library of Munich, Germany, revised 17 Aug 2017.
    8. Stijepic, Denis, 2017. "On the predictability of economic structural change by the Poincaré-Bendixson theory," MPRA Paper 80849, University Library of Munich, Germany, revised 17 Aug 2017.
    9. Stijepic, Denis, 2016. "Empirical evidence on the topological properties of structural paths and some notes on its theoretical explanation," MPRA Paper 82473, University Library of Munich, Germany, revised 26 Oct 2017.
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    Cited by:

    1. Stijepic, Denis, 2019. "A topological approach to structural change analysis and an application to long-run labor allocation dynamics," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 453-462.

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    More about this item

    Keywords

    dynamics; trajectory; 2-simplex; continuous; monotonous; intersection; self-intersection; curvature; Poincaré-Bendixson theory; economics applications;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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