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2011.58: Smoothing non-smooth systems with the moving average transformation

2011.58: Hook James and Dave Broomhead (2011) Smoothing non-smooth systems with the moving average transformation.

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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 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 65 Numerical analysis
MIMS number:2011.58
Deposited By:Mr James Hook
Deposited On:18 August 2011

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