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arXiv · 1306.3648

Non-determinism in the limit of nonsmooth dynamics

Mike R. Jeffrey
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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 discon- tinuous 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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Mike R. Jeffrey. 2013-06-16. Non-determinism in the limit of nonsmooth dynamics. https://doi.org/10.1103/physrevlett.106.254103

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