Namjip Koo

Stability of Linear Dynamic Systems on Time Scales

We examine the various types of stability for the solutions of linear dynamic systems on time scales and give two examples.

Stability for Caputo Fractional Differential Systems

We introduce the notion of h-stability for fractional differential systems. Then we investigate the boundedness and h-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method. Furthermore, we give examples to illustrate our results.

On the stability of linear dynamic systems on time scales

In this paper, we introduce u ∞-similarity in order to unify (continuous) t ∞-similarity and (discrete) n ∞-similarity and then investigate the strong stability for dynamic equations on time scales by using the concept of u ∞-similarity.

Almost Periodic Solutions of Nonlinear Discrete Volterra Equations with Unbounded Delay

We study the existence of almost periodic solutions for nonlinear discrete Volterra equations with unbounded delay, as a discrete analogue of the results for integro-differential equations by Y. Hamaya (1993).

Generic diffeomorphisms with measure-expansive homoclinic classes

We prove that for C1 generic diffeomorphisms, every measure-expansive locally maximal homoclinic class is hyperbolic.

Variationally Asymptotically Stable Difference Systems

We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n∞-summable similarity and comparison principle. Furthermore we study the asymptotic equivalence between nonlinear difference systems and their variational difference systems by means of asymptotic equilibria of two systems.

h-STABILITY FOR NONLINEAR PERTURBED DIFFERENCE SYSTEMS

We show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent by using the concept of -summable similarity of their associated variational systems. Also, we study h-stability for perturbed non-linear system y(n+1) =f(n,y(n)) + g(n,y(n), Sy(n)) of nonlinear difference system x(n+1) =f(n,x(n)) using the comparison principle and extended discrete Bihari-type inequality.

h-Stability of Dynamic Equations on Time Scales with Nonregressivity

We study the -stability of dynamic equations on time scales, without the regressivity condition on the right-hand side of dynamic equations. This means that we can include noninvertible difference equations into our results.

Variationally stable dynamic systems on time scales

In this paper we give a Lyapunov functional characterization of h-stability for nonlinear dynamic systems on time scales under the condition of u∞-similarity between their variational systems. Furthermore, we give some examples related to the notions of u∞-similarity and h-stability.MSC:34N05, 39A30, 34D23, 34K20, 26E70.

Total Stability in Nonlinear Discrete Volterra Equations with Unbounded Delay

We study the total stability in nonlinear discrete Volterra equations with unbounded delay, as a discrete analogue of the results for integrodifferential equations by Y. Hamaya (1990).