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On the Global Structure of a Class of Dynamic Systems
by
R. Rautmann
Paderborn, Germany
In the open positive cone Rn+ of the Euclidian
n-space
Rn we consider a class of nonlinear dynamic systems (*) x' = f(x) having there
a unique critical point x* which can be calculated from a system
of linear equations related to f.
(i) Under a stability condition (being easy to check in
concrete cases) the one-point
set { x* } represents the limit set of all trajectories of (*) in Rn+ , thus x* being
asymptotically and globally stable. With an additional regularity
assumption this stability condition
will become even a necessary one.
(ii) In nonstable cases we get estimates for the domains of attraction
of the origin or the point
at infinity, respectively. Numerical results will be shown in
3-dimensional cases.
Reference: Rautmann, R.: Geometric Aspects of Dynamical
Systems in Rn , Nonlinear
Analysis 47 (2001) 3617-3627.
Date received: January 27, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cajw-94.