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Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations

Kloeden, P. E. and Lorenz, J. (1986) Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations. SIAM Journal on Numerical Analysis, 23 (5). pp. 986-995. ISSN 0036-1429. http://resolver.caltech.edu/CaltechAUTHORS:20120627-134902327

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Abstract

We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set Λ of arbitrary shape. Under the assumption of uniform asymptotic stability of Λ in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets Λ(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of Λ.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/0723066 DOIUNSPECIFIED
http://epubs.siam.org/doi/abs/10.1137/0723066PublisherUNSPECIFIED
Additional Information:© 1986 Society for Industrial and Applied Mathematics. Received by the editors May 28, 1985, and in revised form January 20, 1986. This research was supported by National Science Foundation Grants DMS83-12264 and DMS84-00885, and by U.S. Army contract DAAG29-85-K-0092.
Funders:
Funding AgencyGrant Number
NSFDMS83-12264
NSFDMS84-00885
U. S. Army ContractDAAG29-85-K-0092
Subject Keywords:attracting set; dynamical system; discretization; Lyapunov function
Classification Code:AMS(MOS) subject classifications: 65L05; 34C35
Record Number:CaltechAUTHORS:20120627-134902327
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120627-134902327
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32149
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:27 Jun 2012 23:03
Last Modified:26 Dec 2012 15:25

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