Heterogeneous Models with Learning and Homoclinic Bifurcations

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Heterogenous Agents, Interactions and Economic Performance

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 521))

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Abstract

We analyze a class of models representing heterogeneous agents with adaptively rational rules. The models reduce to non invertible maps of R2. In particular we shall investigate the homoclinic bifurcation of the saddle fixed point, which causes the sudden transition to a chaotic attractor (or strange attractor, with self-similar structure).

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References

  1. Bischi, G.I., Gardini L. (1997) Basin fractalization due to focal points in a class of triangular maps. International Journal of Bifurcations and Chaos, 7

    Google Scholar 

  2. Bischi, G.I., Gardini, L. (2000) Equilibrium selection and transient dynamics under adaptive and statistical learning. Working Paper n.9, Dip. di Economia Università di Parma

    Google Scholar 

  3. Bischi, G.I., Gardini L., Mira, C. (1999) Maps with denominator. Part 1: some generic properties. International Journal of Bifurcation & Chaos, 9:119–153

    Article  Google Scholar 

  4. Brock, W.A., Hommes, C.H. (1995) Rational Route to randomness. Discussion Paper Tinbergen Institute, Amsterdam

    Google Scholar 

  5. Brock, W.A., Hommes, C.H. (1997) A Rational route to randomness. Econometrica, 65:1059–1095

    Article  Google Scholar 

  6. Brock, W.A, Hommes, C.H. (1997) Models of complexity in economics and finance. In Heij, C. et al. (Eds.), System Dynamics in Economic and Financial Models, John Wiley

    Google Scholar 

  7. Brock, W.A., Hommes, C.H. (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. Journal of Economic Dynamics and Control, 22:1235–1274

    Article  Google Scholar 

  8. Chiarella, C., Dieci, R., Gardini, L. (forthcoming) Asset Price Dynamics in a Financial Market with Fundamentalists and Chartists. Discrete Dynamics in Nature and Society

    Google Scholar 

  9. Chiarella, C., Xue-Zhong, He (forthcoming) Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model. Computational Economics

    Google Scholar 

  10. Delli Gatti, D., Gallegati, M., Kirman, A. (2000) Market Structure, Aggregation & Heterogeneity, Cambridge University Press

    Google Scholar 

  11. De Vilder, R. (1996) Complicated Endogenous Business Cycles under Gross Substitutability. Journal of Economic Theory, 71:416–442

    Article  Google Scholar 

  12. De Vilder, R. (2000) On the transition from local regular to global irregular fluctuations. Journal of Economic Dynamics and Control, 24:247–272

    Article  Google Scholar 

  13. Foroni I. (2001) Meccanismi di apprendimento in mercati omogenei ed eterogenei. Phd thesis

    Google Scholar 

  14. Lux, T. (1995) Herd behaviour, bubbles and crashes. The Economic Journal, 105:881–896

    Article  Google Scholar 

  15. Mira, C. (1987) Chaotic Dynamics. From the one-dimensional endomorphism to the two-dimensional diffeomorphism. World Scientific, Singapore

    Google Scholar 

  16. Mira, C., Gardini, L., Barugola, A., Cathala, J.C. (1996) Chaotic Dynamics in Two-Dimensional Noninvertible Maps. World Scientific, Singapore

    Google Scholar 

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Foroni, I., Gardini, L. (2003). Heterogeneous Models with Learning and Homoclinic Bifurcations. In: Cowan, R., Jonard, N. (eds) Heterogenous Agents, Interactions and Economic Performance. Lecture Notes in Economics and Mathematical Systems, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55651-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-55651-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44057-4

  • Online ISBN: 978-3-642-55651-7

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