Bifurcation analysis for the Kaldor–Kalecki model with two delays

Abstract

Abstract In this paper, a Kaldor–Kalecki model of business cycle with two discrete time delays is considered. Firstly, by analyzing the corresponding characteristic equations, the local stability of the positive equilibrium is discussed. Choosing delay (or the adjustment coefficient in the goods market α) as bifurcation parameter, the existence of Hopf bifurcation is investigated in detail. Secondly, by combining the normal form method with the center manifold theorem, we are able to determine the direction of the bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical simulations are carried out to illustrate the theoretical results.

Keywords

• Kaldor–Kalecki model
• Hopf bifurcation
• Stability switch
• Periodic solution
• Two delays