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