title: Nondeterminism in the limit of nonsmooth dynamics.
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.
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, United Kingdom.
authors.forename: Mike R
authors.initials: MR
authors.lastname: Jeffrey
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics