Bistability of equilibria and the 2-tori dynamics in an endogenous growth model undergoing the cusp–Hopf singularity. (February 2018)

• Record Type: Journal Article
• Authors: Bella, Giovanni; Mattana, Paolo
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 185
• Page End: 201
• Publication Date: 2018-02
• Subjects: Multiple BGPs -- Cusp–Hopf bifurcation -- Chaotic dynamics; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.06.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper studies the properties of bistability of equilibria, giving rise to periodic oscillations and 2-tori chaotic dynamics in the full three-dimensional structure of the generalized version of the Chamley (1993) endogenous growth model. This complex dynamic phenomenon reflects a particular hopf bifurcation degeneracy that originates in the neighborhood of a so-called Gavrilov–Guckenheimer singularity, with asymptotical stability properties that lead to persistent oscillations under small perturbations, until a chaos frontier is reached. As a consequence, we study all the necessary conditions, and the exact parametric configuration, that allow to locate the economy on the optimal path that avoids this undesired long run indeterminate solution.