Smoothing non-smooth systems with the moving average transformation

James, Hook and Broomhead, Dave (2011) Smoothing non-smooth systems with the moving average transformation. [MIMS Preprint]

[thumbnail of smoothy.pdf] PDF
smoothy.pdf

Download (859kB)

Abstract

We present a novel, systematic procedure for smoothing non-smooth dynamical systems. In particular we introduce the Moving Average Transformation which can be thought of as a change of variables which transforms discontinuous systems into \emph{dynamically equivalent} continuous systems and continuous but non-differentiable systems into dynamically equivalent differentiable systems. This smoothing gives us a new way to compute the stability properties of a non-smooth systems and provides a new theoretical link between smooth and non-smooth systems. The dynamics and algebraic structure of systems obtained by transforming typical non-smooth systems are investigated.

Item Type: MIMS Preprint
Uncontrolled Keywords: CICADA, non-smooth dynamics, averaging
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Mr James Hook
Date Deposited: 18 Aug 2011
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1664

Actions (login required)

View Item View Item