Economic periodic orbits: a theory of exponential asymptotic stability

Stiefenhofer, Pascal; Giesl, Peter

doi:10.12988/nade.2019.923

Cited by 5 publications

(9 citation statements)

References 7 publications

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“…This problem may prevent economists from deriving analytic solutions of more complex economic problems for the purpose of economic policy analysis. A companion paper revisits the example considered here, and shows that Stiefenhofer and Giesl [8] provide a local theory of exponentially asymptotically stability of nonsmooth periodic orbits and a formula for the basin of attraction, which does not require the calculation of the solution of the dynamical system.…”

Section: Resultsmentioning

confidence: 96%

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A global stability theory of nonsmooth periodic orbits: example I

Stiefenhofer¹,

Giesl²

2019

ams

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Section: Resultsmentioning

confidence: 96%

“…In this paper we compare Poincaré's global stability theory to a local stability theory introduced in Stiefenhofer and Giesl [8], which does not require the calculation of a solution of the system at hand. At the case of an example we compare the two theories.…”

Section: Introductionmentioning

confidence: 99%

A global stability theory of nonsmooth periodic orbits: example I

Stiefenhofer¹,

Giesl²

2019

ams

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“…This dynamical system is introduced in Stiefenhofer and Giesl [8]. On the right-hand side, we provide a condition for switching between economic regimes f ± .…”

Section: The Modelmentioning

confidence: 99%

“…We now investigate the contraction property of the metric function between adjacent solutions, and calculate the ω-limit set of the periodic orbit. The details of how to derive these conditions are given in [8]. In principle, however, our method is a generalization of Borg [9], which introduces the concept of a contraction mapping between adjacent trajectories in the following way:…”

Section: The Modelmentioning

confidence: 99%

Switching Regimes in Economics: The Contraction Mapping and the &omega;-Limit Set

Stiefenhofer

Giesl

2019

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This paper considers a dynamical system defined by a set of ordinary autonomous differential equations with discontinuous right-hand side. Such systems typically appear in economic modelling where there are two or more regimes with a switching between them. Switching between regimes may be a consequence of market forces or deliberately forced in form of policy implementation. Stiefenhofer and Giesl [1] introduce such a model. The purpose of this paper is to show that a metric function defined between two adjacent trajectories contracts in forward time leading to exponentially asymptotically stability of (non)smooth periodic orbits. Hence, we define a local contraction function and distribute it over the smooth and nonsmooth parts of the periodic orbits. The paper shows exponentially asymptotical stability of a periodic orbit using a contraction property of the distance function between two adjacent nonsmooth trajectories over the entire periodic orbit. Moreover it is shown that the ω-limit set of the (non)smooth periodic orbit for two adjacent initial conditions is the same.

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“…In this paper, we aim at establishing existence, uniqueness, and exponentially asymptotically stability of a nonsmooth periodic orbit without its explicit calculation. The theory developed in Stiefenhofer and Giesl [7] allows us to do so. We consider an example and compare our method to Poincaré's theory discussed in a companion paper of this journal.…”

Section: Introductionmentioning

confidence: 99%