## A philosophy for the modelling of realistic nonlinear systems

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- by Phil Howlett, Anatoli Torokhti and Charles Pearce PDF
- Proc. Amer. Math. Soc.
**132**(2004), 353-363 Request permission

## Abstract:

A nonlinear dynamical system is modelled as a nonlinear mapping from a set of input signals into a corresponding set of output signals. Each signal is specified by a set of real number parameters, but such sets may be uncountably infinite. For numerical simulation of the system each signal must be represented by a finite parameter set and the mapping must be defined by a finite arithmetical process. Nevertheless the numerical simulation should be a good approximation to the mathematical model. We discuss the representation of*realistic*dynamical systems and establish a stable approximation theorem for numerical simulation of such systems.

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## Additional Information

**Phil Howlett**- Affiliation: Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes, SA 5095, Australia
- Email: p.howlett@unisa.edu.au
**Anatoli Torokhti**- Affiliation: Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes, SA 5095, Australia.
- Email: a.torokhti@unisa.edu.au
**Charles Pearce**- Affiliation: Department of Applied Mathematics, University of Adelaide, Adelaide, SA 5005, Australia
- Email: cpearce@maths.adelaide.edu.au
- Received by editor(s): September 8, 2000
- Published electronically: August 28, 2003
- Additional Notes: This research was supported by Australian Research Council Grant #A49943121
- Communicated by: Jonathan M. Borwein
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**132**(2004), 353-363 - MSC (2000): Primary 47H99, 47A58; Secondary 37M05
- DOI: https://doi.org/10.1090/S0002-9939-03-07164-8
- MathSciNet review: 2022356