Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 4, Pages 331-337

On (h0,h)-stability of autonomous systems

Xinzhi Liu

University of Waterloo, Department of Applied Mathematics, Ontario, Waterloo N2L 3G1, Canada

Received 1 August 1992; Revised 1 November 1992

Copyright © 1992 Xinzhi Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we discuss the qualitative behavior of a map h along solutions of an autonomous system whose initial values are measured by a second map h0. By doing this, we may deal with, in a unified way, several concepts and associated problems, which are usually considered separately. Five theorems on asymptotic stability are given and two examples are worked out.