Abstract
In Hommes, Nusse, and Simonovits (1990) the dynamics of a simple economic model was studied. Although this piecewise linear model is quite simple, its dynamics shows different kinds of behavior such as periodic, quasiperiodic, and chaotic behavior. In particular, a new kind of bifurcation, namely a period three to period two bifurcation, was observed numerically. This paper deals with this new bifurcation phenomenon and we show that the “period three to period two” bifurcation occurs and is a structurally stable phenomenon in a class of two-dimensional continuous, piecewise linear systems. In particular, the “period three to period two” bifurcation is a structurally stable phenomenon in economic models with Hicksian nonlinearities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Guckenheimer, J., and Holmes, P. (1983):Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. (Applied Mathematical Sciences 42.) New York: Springer-Verlag.
Hommes, C. H., Nusse, H. E., and Simonovits, A. (1990): “Hicksian Cycles and Chaos in a Socialist Economy.” Research Memorandum 382, Institute of Economic Research, University of Groningen.
Yorke, J. A. (1990):DYNAMICS. An Interactive Program for IBM PC Clones. Institute for Physical Science and Technology, University of Maryland.
Author information
Authors and Affiliations
Additional information
Research in part supported by the Department of Energy (Scientific Computing Staff Office of Energy Research).
Rights and permissions
About this article
Cite this article
Hommes, C.H., Nusse, H.E. “Period three to period two” bifurcation for piecewise linear models. Zeitschr. f. Nationalökonomie 54, 157–169 (1991). https://doi.org/10.1007/BF01227083
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01227083