A local stability theory of nonsmooth periodic orbits: example II

Pascal Stiefenhofer; Peter Giesl

doi:10.12988/ams.2019.9464

A local stability theory of nonsmooth periodic orbits: example II

Pascal Stiefenhofer, Peter Giesl

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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 language	English
Journal	Applied Mathematical Sciences
Volume	13
Issue number	11
DOIs	https://doi.org/10.12988/ams.2019.9464
Publication status	Published - 2019

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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 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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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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DO - 10.12988/ams.2019.9464

M3 - Article

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JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

IS - 11

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A local stability theory of nonsmooth periodic orbits: example II

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