A philosophy for the modelling of realistic nonlinear systems

Authors:
Phil Howlett, Anatoli Torokhti and Charles Pearce

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

Published electronically:
August 28, 2003

MathSciNet review:
2022356

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0002-9939-03-07164-8

Keywords:
Operator approximation,
realistic nonlinear systems

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

Article copyright:
© Copyright 2003
American Mathematical Society