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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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.
|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.|
|Subject Keywords:||attracting set; dynamical system; discretization; Lyapunov function|
|Classification Code:||AMS(MOS) subject classifications: 65L05; 34C35|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||27 Jun 2012 23:03|
|Last Modified:||26 Dec 2012 15:25|
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