Nondeterminism in the limit of nonsmooth dynamics

Mike R Jeffrey

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discontinuous derivative can generate multiple outcomes from a single initial state. Here we show that well defined solution sets exist for flows that become multi-valued due to grazing a discontinuity. Loss of determinism is used to quantify dynamics in the limit of infinite sensitivity to initial conditions, then applied to the dynamics of a superconducting resonator and a negatively damped oscillator.
Original languageEnglish
Article number254103
Pages (from-to)1-5
Number of pages5
JournalPhysical Review Letters
Volume106
Issue number25
DOIs
Publication statusPublished - 2011

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dry friction
electronic control
grazing
discontinuity
resonators
oscillators
thresholds
sensitivity

Cite this

Nondeterminism in the limit of nonsmooth dynamics. / Jeffrey, Mike R.

In: Physical Review Letters, Vol. 106, No. 25, 254103, 2011, p. 1-5.

Research output: Contribution to journalArticle

Jeffrey, Mike R. / Nondeterminism in the limit of nonsmooth dynamics. In: Physical Review Letters. 2011 ; Vol. 106, No. 25. pp. 1-5.
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