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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 923809, 29 pages
Research Article

Simple-Zero and Double-Zero Singularities of a Kaldor-Kalecki Model of Business Cycles with Delay

Department of Mathematics, Computer & Information Sciences, Mississippi Valley State University, Itta Bena, MS 38941, USA

Received 12 August 2009; Accepted 2 November 2009

Academic Editor: Xue-Zhong He

Copyright © 2009 Xiaoqin P. Wu. 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.


We study the Kaldor-Kalecki model of business cycles with delay in both the gross product and the capital stock. Simple-zero and double-zero singularities are investigated when bifurcation parameters change near certain critical values. By performing center manifold reduction, the normal forms on the center manifold are derived to obtain the bifurcation diagrams of the model such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.