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Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces

Research output: Contribution to journalArticle

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Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces. / Jeffrey, M. R.; Kafanas, G.; Simpson, D. J.W.

In: International Journal of Bifurcation and Chaos, Vol. 28, No. 6, 1830020, 15.06.2018.

Research output: Contribution to journalArticle

Harvard

Jeffrey, MR, Kafanas, G & Simpson, DJW 2018, 'Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces', International Journal of Bifurcation and Chaos, vol. 28, no. 6, 1830020. https://doi.org/10.1142/S0218127418300203

APA

Jeffrey, M. R., Kafanas, G., & Simpson, D. J. W. (2018). Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces. International Journal of Bifurcation and Chaos, 28(6), [1830020]. https://doi.org/10.1142/S0218127418300203

Vancouver

Jeffrey MR, Kafanas G, Simpson DJW. Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces. International Journal of Bifurcation and Chaos. 2018 Jun 15;28(6). 1830020. https://doi.org/10.1142/S0218127418300203

Author

Jeffrey, M. R. ; Kafanas, G. ; Simpson, D. J.W. / Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces. In: International Journal of Bifurcation and Chaos. 2018 ; Vol. 28, No. 6.

Bibtex

@article{01665936d4394f399cc4b7b31ac20292,
title = "Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces",
abstract = "Differential equations that switch between different modes of behavior across a surface of discontinuity are used to model, for example, electronic switches, mechanical contact, predator-prey preference changes, and genetic or cellular regulation. Switching in such systems is unlikely to occur precisely at the ideal discontinuity surface, but instead can involve various spatiotemporal delays or noise. If a system switches between more than two modes, across a boundary formed by the intersection of discontinuity surfaces, then its motion along that intersection becomes highly sensitive to such nonidealities. If switching across the surfaces is affected by hysteresis, time delay, or discretization, then motion along the intersection can be affected by erratic variations that we characterize as {"}jitter{"}. Introducing noise, or smoothing out the discontinuity, instead leads to steady motion along the intersection well described by the so-called canopy extension of Filippov's sliding concept (which applies when the discontinuity surface is a simple hypersurface). We illustrate the results with numerical experiments and an example from power electronics, providing explanations for the phenomenon as far as they are known.",
keywords = "Discontinuity, dynamics, intersection, jitter, modeling, sliding, switching",
author = "Jeffrey, {M. R.} and G. Kafanas and Simpson, {D. J.W.}",
year = "2018",
month = "6",
day = "15",
doi = "10.1142/S0218127418300203",
language = "English",
volume = "28",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "World Scientific Publishing Co.",
number = "6",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Jitter in Piecewise-Smooth Dynamical Systems with Intersecting Discontinuity Surfaces

AU - Jeffrey, M. R.

AU - Kafanas, G.

AU - Simpson, D. J.W.

PY - 2018/6/15

Y1 - 2018/6/15

N2 - Differential equations that switch between different modes of behavior across a surface of discontinuity are used to model, for example, electronic switches, mechanical contact, predator-prey preference changes, and genetic or cellular regulation. Switching in such systems is unlikely to occur precisely at the ideal discontinuity surface, but instead can involve various spatiotemporal delays or noise. If a system switches between more than two modes, across a boundary formed by the intersection of discontinuity surfaces, then its motion along that intersection becomes highly sensitive to such nonidealities. If switching across the surfaces is affected by hysteresis, time delay, or discretization, then motion along the intersection can be affected by erratic variations that we characterize as "jitter". Introducing noise, or smoothing out the discontinuity, instead leads to steady motion along the intersection well described by the so-called canopy extension of Filippov's sliding concept (which applies when the discontinuity surface is a simple hypersurface). We illustrate the results with numerical experiments and an example from power electronics, providing explanations for the phenomenon as far as they are known.

AB - Differential equations that switch between different modes of behavior across a surface of discontinuity are used to model, for example, electronic switches, mechanical contact, predator-prey preference changes, and genetic or cellular regulation. Switching in such systems is unlikely to occur precisely at the ideal discontinuity surface, but instead can involve various spatiotemporal delays or noise. If a system switches between more than two modes, across a boundary formed by the intersection of discontinuity surfaces, then its motion along that intersection becomes highly sensitive to such nonidealities. If switching across the surfaces is affected by hysteresis, time delay, or discretization, then motion along the intersection can be affected by erratic variations that we characterize as "jitter". Introducing noise, or smoothing out the discontinuity, instead leads to steady motion along the intersection well described by the so-called canopy extension of Filippov's sliding concept (which applies when the discontinuity surface is a simple hypersurface). We illustrate the results with numerical experiments and an example from power electronics, providing explanations for the phenomenon as far as they are known.

KW - Discontinuity

KW - dynamics

KW - intersection

KW - jitter

KW - modeling

KW - sliding

KW - switching

UR - http://www.scopus.com/inward/record.url?scp=85048985702&partnerID=8YFLogxK

U2 - 10.1142/S0218127418300203

DO - 10.1142/S0218127418300203

M3 - Article

VL - 28

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 6

M1 - 1830020

ER -