A local stability theory of nonsmooth periodic orbits: example II

Pascal Stiefenhofer, Peter Giesl

Research output: Contribution to journalArticleResearchpeer-review

Abstract

This paper considers an application of a local theory of exponentially asymptotically stability of nonsmooth periodic orbits derived from a planar dynamical system of autonomous ordinary differential equations with discontinuous right-hand side. Such dynamical systems are encountered in economic modelling in the context of economic growth. In this paper, we revisit an example considered in a companion paper of
this journal and show that the explicit solution of the dynamical system is not required in showing exponentially asymptotically stability. We also provide a formula for the basin of attraction. The cost of the new method is also assessed.
Original languageEnglish
JournalApplied Mathematical Sciences
Volume13
Issue number11
DOIs
Publication statusPublished - 2019

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Stability Theory
Local Stability
Periodic Orbits
Dynamical system
Economic Growth
Basin of Attraction
Explicit Solution
Ordinary differential equation
Economics
Costs
Modeling

Bibliographical note

This article is distributed under the Creative Commons by-nc-nd Attribution License. Copyright 2019 Hikari Ltd.

Cite this

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A local stability theory of nonsmooth periodic orbits : example II. / Stiefenhofer, Pascal; Giesl, Peter.

In: Applied Mathematical Sciences, Vol. 13, No. 11, 2019.

Research output: Contribution to journalArticleResearchpeer-review

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AB - This paper considers an application of a local theory of exponentially asymptotically stability of nonsmooth periodic orbits derived from a planar dynamical system of autonomous ordinary differential equations with discontinuous right-hand side. Such dynamical systems are encountered in economic modelling in the context of economic growth. In this paper, we revisit an example considered in a companion paper ofthis journal and show that the explicit solution of the dynamical system is not required in showing exponentially asymptotically stability. We also provide a formula for the basin of attraction. The cost of the new method is also assessed.

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