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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 312574, 14 pages
http://dx.doi.org/10.1155/2015/312574
Research Article

The Asymptotic Behavior in a Nonlinear Cobweb Model with Time Delays

1Department of Economics, International Center for Further Development of Dynamic Economic Research, Chuo University, 742-1 Higashi-Nakano, Hachioji, Tokyo 192-0393, Japan
2Department of Applied Mathematics, University of Pécs, Ifjúság Útja 6, Pécs 7624, Hungary

Received 24 March 2015; Accepted 29 June 2015

Academic Editor: Peng Shi

Copyright © 2015 Akio Matsumoto and Ferenc Szidarovszky. 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

We study the effects of production delays on the local as well as global dynamics of nonlinear cobweb models in a continuous-time framework. After reviewing a single delay model, we proceed to two models with two delays. When the two delays are used to form an expected price or feedback for price adjustment, we have a winding stability switching curve and in consequence obtain repetition of stability losses and gains via Hopf bifurcation. When the two delays are involved in two interrelated markets, we find that the stability switching occurs on straight lines and complicated dynamics can arise in unstable markets.