Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 509561, 18 pages
doi:10.1155/2009/509561
Research Article
A Dynamic Economic Model with Discrete Time and Consumer Sentiment
1Australian School of Business, University of New South Wales, Sydney NSW 2052, Australia
2Department of Economic Informatics, Mathematics and Statistics, Faculty of Economics, West University of Timişoara, 16A Pestalozzi Street, 300115 Timişoara, Romania
3Department of Mathematics, Politehnica University of Timişoara, 2 P-ţa. Victoriei, 300004 Timişoara, Romania
4Department of Applied Mathematics, Faculty of Mathematics, West University of Timişoara, 4 V. Parvan Street, 300223 Timişoara, Romania
Received 21 September 2009; Accepted 1 December 2009
Academic Editor: Akio Matsumoto
Copyright © 2009 L. I. Dobrescu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The paper describes a dynamical economic model with discrete time and consumer sentiment in the deterministic and stochastic cases. We seek to demonstrate that consumer sentiment may create fluctuations in the economical activities. The model possesses a flip bifurcation and a Neimark-Sacker bifurcation, after which the stable state
is replaced by a (quasi) periodic motion. We associate the difference stochastic equation to the model by randomizing the control parameter d and by adding one stochastic control. Numerical simulations are made for the deterministic and stochastic models, for different values of the control parameter d.