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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. doi:10.1137/0723066.

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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.

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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.
Funding AgencyGrant Number
U. S. Army ContractDAAG29-85-K-0092
Subject Keywords:attracting set; dynamical system; discretization; Lyapunov function
Issue or Number:5
Classification Code:AMS(MOS) subject classifications: 65L05; 34C35
Record Number:CaltechAUTHORS:20120627-134902327
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32149
Deposited By: Jason Perez
Deposited On:27 Jun 2012 23:03
Last Modified:09 Nov 2021 21:25

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