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Modeling with nonsmooth dynamics

Research output: Book/ReportAuthored book

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Modeling with nonsmooth dynamics. / Jeffrey, Mike R.

Springer, 2019. 108 p. (Frontiers in applied dynamical systems).

Research output: Book/ReportAuthored book

Harvard

Jeffrey, MR 2019, Modeling with nonsmooth dynamics. Frontiers in applied dynamical systems, Springer. https://doi.org/10.1007/978-3-030-35987-4

APA

Jeffrey, M. R. (Accepted/In press). Modeling with nonsmooth dynamics. (Frontiers in applied dynamical systems). Springer. https://doi.org/10.1007/978-3-030-35987-4

Vancouver

Jeffrey MR. Modeling with nonsmooth dynamics. Springer, 2019. 108 p. (Frontiers in applied dynamical systems). https://doi.org/10.1007/978-3-030-35987-4

Author

Jeffrey, Mike R. / Modeling with nonsmooth dynamics. Springer, 2019. 108 p. (Frontiers in applied dynamical systems).

Bibtex

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title = "Modeling with nonsmooth dynamics",
abstract = "As mathematics is applied to model ever new problems in engi- neering and the life sciences, increasing use is being made of systems that switch between different sets of equations on distinct domains. To find their dynamics requires the discontinuity between domains to be resolved or ‘regularized’ in some way, and there exist a range of methods to do so. Some preserve the ideal character of the disconti- nuity as a piecewise-smooth system (giving e.g. ‘impact’ or ‘switching’ dynamics), while others blur the discontinuity by smoothing it out, or introducing overshoots due to deterministic or stochastic delays.Despite exciting new applications and major theoretical advances, it remains unclear how widely applicable nonsmooth models are, or in what sense they approximate discontinuities in real world systems. It is even unclear how to correctly simulate or solve nonsmooth systems, or how robust such solutions are to perturbation. To move closer towards these goals, here we survey one of the main approaches to modeling nonsmooth dynamics, and look at how loosening some of its rigourous but idealized framework allows us to probe its modeling assumptions. We also draw together a range of phenomena that characterize the sensitivity and robustness of nonsmooth dynamical models.",
author = "Jeffrey, {Mike R}",
year = "2019",
month = "9",
day = "3",
doi = "10.1007/978-3-030-35987-4",
language = "English",
isbn = "978-3-030-35986-7",
series = "Frontiers in applied dynamical systems",
publisher = "Springer",

}

RIS - suitable for import to EndNote

TY - BOOK

T1 - Modeling with nonsmooth dynamics

AU - Jeffrey, Mike R

PY - 2019/9/3

Y1 - 2019/9/3

N2 - As mathematics is applied to model ever new problems in engi- neering and the life sciences, increasing use is being made of systems that switch between different sets of equations on distinct domains. To find their dynamics requires the discontinuity between domains to be resolved or ‘regularized’ in some way, and there exist a range of methods to do so. Some preserve the ideal character of the disconti- nuity as a piecewise-smooth system (giving e.g. ‘impact’ or ‘switching’ dynamics), while others blur the discontinuity by smoothing it out, or introducing overshoots due to deterministic or stochastic delays.Despite exciting new applications and major theoretical advances, it remains unclear how widely applicable nonsmooth models are, or in what sense they approximate discontinuities in real world systems. It is even unclear how to correctly simulate or solve nonsmooth systems, or how robust such solutions are to perturbation. To move closer towards these goals, here we survey one of the main approaches to modeling nonsmooth dynamics, and look at how loosening some of its rigourous but idealized framework allows us to probe its modeling assumptions. We also draw together a range of phenomena that characterize the sensitivity and robustness of nonsmooth dynamical models.

AB - As mathematics is applied to model ever new problems in engi- neering and the life sciences, increasing use is being made of systems that switch between different sets of equations on distinct domains. To find their dynamics requires the discontinuity between domains to be resolved or ‘regularized’ in some way, and there exist a range of methods to do so. Some preserve the ideal character of the disconti- nuity as a piecewise-smooth system (giving e.g. ‘impact’ or ‘switching’ dynamics), while others blur the discontinuity by smoothing it out, or introducing overshoots due to deterministic or stochastic delays.Despite exciting new applications and major theoretical advances, it remains unclear how widely applicable nonsmooth models are, or in what sense they approximate discontinuities in real world systems. It is even unclear how to correctly simulate or solve nonsmooth systems, or how robust such solutions are to perturbation. To move closer towards these goals, here we survey one of the main approaches to modeling nonsmooth dynamics, and look at how loosening some of its rigourous but idealized framework allows us to probe its modeling assumptions. We also draw together a range of phenomena that characterize the sensitivity and robustness of nonsmooth dynamical models.

U2 - 10.1007/978-3-030-35987-4

DO - 10.1007/978-3-030-35987-4

M3 - Authored book

SN - 978-3-030-35986-7

T3 - Frontiers in applied dynamical systems

BT - Modeling with nonsmooth dynamics

PB - Springer

ER -