Into higher dimensions for nonsmooth dynamical systems

Mike R Jeffrey; Thomas Seidman; Marco Antonio Teixeira; Vadim Utkin

doi:10.1016/j.physd.2022.133222

Into higher dimensions for nonsmooth dynamical systems

Mike R Jeffrey, Thomas Seidman, Marco Antonio Teixeira, Vadim Utkin

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Abstract

The study of nonsmooth dynamical systems is reaching a turning point. As the theory of bifurcations and chaos in low dimensions appear now to be coming of age, attention is turning to higher dimensions. This brings new challenges for the concept of solutions of a nonsmooth system with multiple dimensions and complex discontinuity geometries. There are a range of solution concepts for nonsmooth systems, and here we highlight how each is valid in different contexts, we discuss the extent to which they are consistent, and that only together do they allow us to tackle higher dimensional nonsmooth systems with a view to applications.

Original language	English
Article number	133222
Journal	Physica D: Nonlinear Phenomena
Volume	434
Early online date	28 Mar 2022
DOIs	https://doi.org/10.1016/j.physd.2022.133222
Publication status	Published - 1 Jun 2022

Bibliographical note

Funding Information:
MAT is partially supported by a CNPq grant 301275/2017-3 .

Publisher Copyright:
© 2022 Elsevier B.V.

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Engineering Mathematics Research Group

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10.1016/j.physd.2022.133222

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abstract = "The study of nonsmooth dynamical systems is reaching a turning point. As the theory of bifurcations and chaos in low dimensions appear now to be coming of age, attention is turning to higher dimensions. This brings new challenges for the concept of solutions of a nonsmooth system with multiple dimensions and complex discontinuity geometries. There are a range of solution concepts for nonsmooth systems, and here we highlight how each is valid in different contexts, we discuss the extent to which they are consistent, and that only together do they allow us to tackle higher dimensional nonsmooth systems with a view to applications.",

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AU - Seidman, Thomas

AU - Teixeira, Marco Antonio

AU - Utkin, Vadim

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Y1 - 2022/6/1

N2 - The study of nonsmooth dynamical systems is reaching a turning point. As the theory of bifurcations and chaos in low dimensions appear now to be coming of age, attention is turning to higher dimensions. This brings new challenges for the concept of solutions of a nonsmooth system with multiple dimensions and complex discontinuity geometries. There are a range of solution concepts for nonsmooth systems, and here we highlight how each is valid in different contexts, we discuss the extent to which they are consistent, and that only together do they allow us to tackle higher dimensional nonsmooth systems with a view to applications.

AB - The study of nonsmooth dynamical systems is reaching a turning point. As the theory of bifurcations and chaos in low dimensions appear now to be coming of age, attention is turning to higher dimensions. This brings new challenges for the concept of solutions of a nonsmooth system with multiple dimensions and complex discontinuity geometries. There are a range of solution concepts for nonsmooth systems, and here we highlight how each is valid in different contexts, we discuss the extent to which they are consistent, and that only together do they allow us to tackle higher dimensional nonsmooth systems with a view to applications.

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DO - 10.1016/j.physd.2022.133222

M3 - Article (Academic Journal)

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

M1 - 133222

ER -

Into higher dimensions for nonsmooth dynamical systems

Abstract

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