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RESEARCH CENTER
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Working Paper-
ISCTE
Lisbon University Institute
Controlling Endogenous Cycles
Vivaldo M. Mendes
in an OLG Economy
Diana A. Mendes
Working Paper - 08/08
- Lisbon University Institute
by the OGY Method
Controlling Endogenous Cycles in an OLG
Economy by the OGY Method
Vivaldo Mendes1 and Diana A. Mendes2
ISCTE, Lisbon
September, 2007
1Corresponding author. Department of Economics, ISCTE, and UNIDE-ISCTE.
Electronic address: vivaldo.mendes@iscte.pt.
2Department of Quantitative Methods, ISCTE and UNIDE-ISCTE. Electronic ad-
dress: diana.mendes@iscte.pt.
Abstract
We show that very complicated dynamics arising, e.g.
from an overlapping
generations model (OLG) with production and an endogenous intertemporal
decision between labour and leisure, which produces hyperchaos (both eigenval-
ues with modulus higher than 1), can in fact be controlled or managed with
relative simplicity. The aperiodic and very complicated motion that stems from
this model can be subject to control by very small perturbations in its parame-
ters and turned into a stable steady state or into a regular cycle. Therefore, the
system can be controlled without a change of its original properties. To per-
form the control of chaos in this economic model we apply the pole-placement
technique, developed by Romeiras, Grebogi, Ott and Dayawansa (1992).
The application of control methods to chaotic economic dynamics may raise se-
rious reservations, at least on mathematical and logical grounds, to some recent
views on economics which have argued that economic policy becomes useless in
the presence of chaotic motion (and thus, that the performance of the economic
system cannot be improved by public intervention, i.e., that the amplitude of
cycles cannot be controlled or reduced). In fact, the ne tuning of the system
(that is, the control) can be performed without having to rely only on inni-
tesimal accuracy in the perturbation