A philosophy for the modelling of realistic nonlinear systems
Authors:
Phil Howlett, Anatoli Torokhti and Charles Pearce
Journal:
Proc. Amer. Math. Soc. 132 (2004), 353363
MSC (2000):
Primary 47H99, 47A58; Secondary 37M05
Published electronically:
August 28, 2003
MathSciNet review:
2022356
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002993903071648
PII:
S 00029939(03)071648
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
