Nondeterminism in the limit of nonsmooth dynamics

Reference:

Jeffrey, M. R., 2011. Nondeterminism in the limit of nonsmooth dynamics. Physical Review Letters, 106 (25), 254103.

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Official URL:

http://dx.doi.org/10.1103/PhysRevLett.106.254103

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.

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