A Krawiec-Szydlowski Model of Business Cycles with a Time Delay in Capital Stock



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In this paper, a Krawiec-Szydlowski model of business cycles with delay in the capital stock is studied. The distribution of roots of the characteristic equation at the equilibrium point is studied and the conditions to have a pair of purely imaginary roots, a simple zero root and a double-zero root are given. Hopf and Bogdanov–Takens (BT) bifurcations are investigated and their corresponding normal forms are obtained when the characteristic equation has a pair of purely imaginary roots and a double-zero root, respectively. For Hopf bifurcation, the direction and the stability of the limit cycle are given. For BT bifurcation, the bifurcation diagrams are given. Some examples are given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]