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

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 tha...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.926-933-890
Main Authors: Ballestra, Luca Vincenzo, Guerrini, Luca, Pacelli, Graziella
Format: Article
Language:English
Subjects:
Bifurcation theory
Business
Business cycles
Delay
Delay equations
Differential equations
Differential equations, Nonlinear
Dynamical systems
Hopf bifurcation
Mathematical analysis
Mathematical models
Mathematical research
Stability
Switches
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/689372