Nondeterminism in the limit of nonsmooth dynamics

Mike R Jeffrey

Research output: Contribution to journalArticlepeer-review

33 Citations (SciVal)


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
Issue number25
Publication statusPublished - 2011


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