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

Luca Vincenzo Ballestra | Zendy; Luca Guerrini | Zendy; Graziella Pacelli | Zendy

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

Author(s) -

Luca Vincenzo Ballestra,

Luca Guerrini,

Graziella Pacelli

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/689372

Subject(s) - mathematics , hopf bifurcation , center manifold , transcendental equation , mathematical analysis , stability (learning theory) , saddle node bifurcation , bifurcation diagram , biological applications of bifurcation theory , bifurcation , pitchfork bifurcation , differential equation , nonlinear system , physics , quantum mechanics , machine learning , computer science

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

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