[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2004.41.4.665

ASYMPTOTIC STABILITY IN GENERAL DYNAMICAL SYSTEMS

Lim, Young-Il (Department of Mathematics, Hoseo University)
Lee, Kyung-Bok (Department of Mathematics, Hoseo University)
Park, Jong-Soh (Department of Mathematics, Chungnam National University)

Publication Information

Bulletin of the Korean Mathematical Society / v.41, no.4, 2004 , pp. 665-676 More about this Journal

Abstract

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

Keywords

C-first countable space; asymptotic stability; general dynamical systems; Lyapunov function and strict Lyapunov function;

Citations & Related Records

Reference

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