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Nondeterminism in the Limit of Nonsmooth Dynamics

Mike R. Jeffrey
Phys. Rev. Lett. 106, 254103 – Published 24 June 2011
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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 multivalued 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.

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  • Received 1 April 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.254103

© 2011 American Physical Society

Authors & Affiliations

Mike R. Jeffrey

  • Department of Engineering Mathematics, University of Bristol, Queen’s Building, Bristol BS8 1TR, United Kingdom

See Also

Generating Chaos in a New Way

Mark Buchanan
Phys. Rev. Focus 28, 1 (2011)

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Issue

Vol. 106, Iss. 25 — 24 June 2011

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