Non-determinism in the limit of nonsmooth dynamics
Dynamical Systems
2013-06-18 v1
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.
Cite
@article{arxiv.1306.3648,
title = {Non-determinism in the limit of nonsmooth dynamics},
author = {Mike R. Jeffrey},
journal= {arXiv preprint arXiv:1306.3648},
year = {2013}
}