摘要
本文讨论动力系统的Ｌｉｐｓｃｈｉｔｚ稳定性与吸引性之间的关系．给出动力系统中弱吸引性、吸引性和强吸引性这三个概念相互等价的条件，在一定的条件下证明了（弱、强）吸引子与全局（弱、强）吸引子是一致的．本文还讨论了度量Ｌｙａｐｕｎｏｖ稳定性和拓扑Ｌｙａｐｕｎｏｖ稳定性及它们与Ｌｉｐｓｃｈｉｔｚ稳定性之间的关系．
The main purpose of this papet is to discuss the relationship between attraction andLipschitz stability in dynamical systems. Some conditions are given for the pairwise equivalencesamong the three notions of weak attraction,attraction and strong attraction. Under certainconditions, it is shown that the notions of an(a Weak,strong)attractor and a global(weak,strong)attractor coincide .Also, we investigate the metric and topological Lyapunov stability and their relations with Lipschitz stability.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1995年第5期621-627,共7页
Acta Mathematica Sinica：Chinese Series
基金
煤炭院校优秀青年基金
关键词
动力系统
正向极限集
李普希兹稳定性
吸引子
dynamical system,positive Lipschitz stability,positive limit set, positive prolonga-tional limit set, attractor, metric Lyapunov stability
