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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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
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
Bischi, G.I., Gardini L., Mira, C. (1999) Maps with denominator. Part 1: some generic properties. International Journal of Bifurcation & Chaos, 9:119–153
Brock, W.A., Hommes, C.H. (1995) Rational Route to randomness. Discussion Paper Tinbergen Institute, Amsterdam
Brock, W.A., Hommes, C.H. (1997) A Rational route to randomness. Econometrica, 65:1059–1095
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
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
Chiarella, C., Dieci, R., Gardini, L. (forthcoming) Asset Price Dynamics in a Financial Market with Fundamentalists and Chartists. Discrete Dynamics in Nature and Society
Chiarella, C., Xue-Zhong, He (forthcoming) Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model. Computational Economics
Delli Gatti, D., Gallegati, M., Kirman, A. (2000) Market Structure, Aggregation & Heterogeneity, Cambridge University Press
De Vilder, R. (1996) Complicated Endogenous Business Cycles under Gross Substitutability. Journal of Economic Theory, 71:416–442
De Vilder, R. (2000) On the transition from local regular to global irregular fluctuations. Journal of Economic Dynamics and Control, 24:247–272
Foroni I. (2001) Meccanismi di apprendimento in mercati omogenei ed eterogenei. Phd thesis
Lux, T. (1995) Herd behaviour, bubbles and crashes. The Economic Journal, 105:881–896
Mira, C. (1987) Chaotic Dynamics. From the one-dimensional endomorphism to the two-dimensional diffeomorphism. World Scientific, Singapore
Mira, C., Gardini, L., Barugola, A., Cathala, J.C. (1996) Chaotic Dynamics in Two-Dimensional Noninvertible Maps. World Scientific, Singapore
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Springer Book Archive