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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.

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File URL: http://mpra.ub.uni-muenchen.de/50814/
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File URL: http://mpra.ub.uni-muenchen.de/56970/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 50814.

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Date of creation: Feb 2013
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Handle: RePEc:pra:mprapa:50814

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Keywords: Andronov-Hopf bifurcation; Limit cycles;

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  1. K. Vela Velupillai, 2004. "A Disequilibrium Macrodynamic Model of Fluctuations," Working Papers 0081, National University of Ireland Galway, Department of Economics, revised 2004.
  2. 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 589-96, October.
  3. 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.
  4. 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.
  5. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
  6. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
  7. 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 242-56, April.
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