Sung Kyu Choi

Recurrence in persistent dynamical systems

The purpose of this paper is to study the chain recurrent sets under persistent dynamical systems, and give a necessary condition for a persistent dynamical system to be topologically stable. Moreover we show that the various recurrent sets depend continuously on persistent dynamical systems.

ASYMPTOTIC EQUIVALENCE FOR LINEAR DIFFERENTIAL SYSTEMS

We investigate the asymptotic equivalence for linear differen- tial systems by means of the notions of t1 -similarity and strong stability.

ASYMPTOTIC EQUIVALENCE BETWEEN TWO LINEAR DYNAMIC SYSTEMS ON TIME SCALES

Abstract. In this paper we investigate asymptotic properties about as-ymptotic equilibrium and asymptotic equivalence for linear dynamic sys-tems on time scales by using the notion of u ∞ -similarity. Also, we givesome examples to illustrate our results. 1. IntroductionThe calculus on time scales was initiated by Aulbach and Hilger in orderto create a theory that can unify and extend discrete and continuous analysis[1, 2, 15]. The theory on time scales has been developed as a generalization ofboth continuous and discrete time theory and applied to many different fieldsof mathematics [1, 2, 3, 4].The notion of similarity is an effective tool to study the theory of stabilityfor differential systems and difference systems [5, 7, 10, 11, 12, 17, 18, 19].Markus [17] introduced the notion of kinematic similarity in the set of alln×n continuous matrices defined on [t 0 ,∞) and showed that the relationshipof kinematic similarity is an equivalence relation preserving the type numbersof the linear differential systems. Gohberg et al. [14] studied the problemto classify linear time-varying systems of difference equations under kinematicsimilarity. Conti [12] introduced the concept of t

Impulsive Stabilization of Dynamic Equations on Time Scales

In this paper we study the impulsive stabilization of dynamic equations on time scales via the Lyapunov’s direct method. Our results show that dynamic equations on time scales may be -exponentially stabilized by impulses. Furthermore, we give some examples to illustrate our results.