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On the transition from local regular to global irregular fluctuations

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  • P. Pintus
  • D. Sands
  • R. de Vilder

Abstract

We present a general framework for understanding the transition from local regular to global irregular (chaotic) behavior of nonlinear dynamical models in discrete time. The fundamental mechanism is the unfolding of quadratic tangencies between the stable and the unstable manifolds of periodic saddle points. To illustrate the relevance of the presented methods for analyzing globally a class of dynamic economic models, we apply them to the finite horizon model of Woodford.

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Bibliographic Info

Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 98-18.

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Date of creation: 1998
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Handle: RePEc:ema:worpap:98-18

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  1. Benhabib, Jess & Laroque, Guy, 1988. "On competitive cycles in productive economies," Journal of Economic Theory, Elsevier, vol. 45(1), pages 145-170, June.
  2. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
  3. Brock, W.A. & Hommes, C.H., 1996. "A Rational Route to Randomness," Working papers 9530r, Wisconsin Madison - Social Systems.
  4. Cazzavillan, Guido & Lloyd-Braga, Teresa & Pintus, Patrick, 1996. "Multiple steady states and endogenous fluctuations with increasing returns to scale in production," CEPREMAP Working Papers (Couverture Orange) 9618, CEPREMAP.
  5. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
  6. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
  7. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, October.
  8. Farmer, Roger E. A., 1986. "Deficits and cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 77-88, October.
  9. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
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