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Języki publikacji
Abstrakty
We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit set consists of rest points, and if a trajectory in a locally compact space is uniformly asymptotically Zhukovskiĭ quasi-stable, then its limit set is a rest point or a periodic orbit. Also, we present examples to show the differences between variant quasi-stabilities. Further, some sufficient conditions are given to guarantee the quasi-stabilities of a prescribed trajectory.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
139-154
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
- School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P.R. China
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-2-4