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Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems

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  • Datta, Soumya

Abstract

Using a macroeconomic example, the paper proposes an algorithm to symbolically construct the topological normal form of Andronov-Hopf bifurcation. It also offers a program, using the Computer Algebra System `Maxima', to apply this algorithm. In case the limit cycle turns out to be unstable, the possibilities of the dynamics converging to another limit cycle is explored.

Suggested Citation

  • Datta, Soumya, 2013. "Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems," MPRA Paper 50814, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:50814
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    File URL: https://mpra.ub.uni-muenchen.de/56970/9/MPRA_paper_56970.pdf
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    References listed on IDEAS

    as
    1. Chiarella,Carl & Flaschel,Peter, 2011. "The Dynamics of Keynesian Monetary Growth," Cambridge Books, Cambridge University Press, number 9780521180184, January.
    2. Velupillai, K. Vela, 2006. "A disequilibrium macrodynamic model of fluctuations," Journal of Macroeconomics, Elsevier, vol. 28(4), pages 752-767, December.
    3. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
    4. Benhabib, Jess & Miyao, Takahiro, 1981. "Some New Results on the Dynamics of the Generalized Tobin Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 589-596, October.
    5. William A. Barnett & Yijun He, 1998. "Bifurcations in Continuous-Time Macroeconomic Systems," Macroeconomics 9805018, University Library of Munich, Germany.
    6. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    7. William Barnett & Yijun He, 2006. "Existence of Bifurcation in Macroeconomic Dynamics: Grandmont was Right," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200610, University of Kansas, Department of Economics.
    8. Asada, Toichiro & Chen, Pu & Chiarella, Carl & Flaschel, Peter, 2006. "Keynesian dynamics and the wage-price spiral: A baseline disequilibrium model," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 90-130, March.
    9. Datta, Soumya, 2012. "Cycles and Crises in a Model of Debt-financed Investment-led Growth," MPRA Paper 50200, University Library of Munich, Germany, revised 12 Dec 2012.
    10. Chiarella,Carl & Flaschel,Peter & Franke,Reiner, 2011. "Foundations for a Disequilibrium Theory of the Business Cycle," Cambridge Books, Cambridge University Press, number 9780521369923, January.
    11. Franke, Reiner, 1992. "Stable, Unstable, and Persistent Cyclical Behaviour in a Keynes-Wicksell Monetary Growth Model," Oxford Economic Papers, Oxford University Press, vol. 44(2), pages 242-256, April.
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    Cited by:

    1. Yannis Dafermos, 2018. "Debt cycles, instability and fiscal rules: a Godley–Minsky synthesis," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 42(5), pages 1277-1313.
    2. Datta, Soumya, 2012. "Cycles and Crises in a Model of Debt-financed Investment-led Growth," MPRA Paper 50200, University Library of Munich, Germany, revised 12 Dec 2012.

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    More about this item

    Keywords

    Andronov-Hopf bifurcation; Limit cycles;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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