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.
Bistability of equilibria and the 2-tori dynamics in an endogenous growth model undergoing the cusp–Hopf singularity
BELLA, GIOVANNI;MATTANA, PAOLO
2018-01-01
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.File | Dimensione | Formato | |
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