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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 689372, 8 pages
http://dx.doi.org/10.1155/2013/689372
Research Article

Stability Switches and Hopf Bifurcation in a Kaleckian Model of Business Cycle

1Department of Economics, Second University of Naples, 81043 Capua, Italy
2Department of Management, Polytechnic University of Marche, 60121 Ancona, Italy

Received 11 July 2013; Accepted 23 July 2013

Academic Editor: Massimiliano Ferrara

Copyright © 2013 Luca Vincenzo Ballestra 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

This paper considers a Kaleckian type model of business cycle based on a nonlinear delay differential equation, whose associated characteristic equation is a transcendental equation with delay dependent coefficients. Using the conventional analysis introduced by Beretta and Kuang (2002), we show that the unique equilibrium can be destabilized through a Hopf bifurcation and stability switches may occur. Then some properties of Hopf bifurcation such as direction, stability, and period are determined by the normal form theory and the center manifold theorem.