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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: August 28, 2003
MathSciNet review: 2022356
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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: http://dx.doi.org/10.1090/S0002-9939-03-07164-8
PII: S 0002-9939(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