• Computers and Concrete
• /
• v.30 no.4
• /
• pp.237-242
• /
• 2022

This paper is concerned with exponential stability in mean square for stochastic static neutral neural networks with varying delays. By using Lyapunov functional method and with the help of stochastic analysis technique, the sufficient conditions to guarantee the exponential stability in mean square for the neural networks are obtained and some results of related literature are extended.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.295-301
• /
• 2009

We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings f, g, h : $G{\times}S{\rightarrow}{\mathbb{C}}$, where G is an abelian group and S is a commutative semigroup which is divisible by 2. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.

• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.851-864
• /
• 2017

The problems of global and local exponential stability analysis of a class of nonlinear non-autonomous difference equations in Banach spaces are studied in this paper. By a novel comparison technique, new explicit exponential stability conditions are derived. Numerical examples are given to illustrate the effectiveness of the obtained results.

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.449-463
• /
• 1998

In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^{r}$ dynamical systems (or $C^{r}$ diffeomor-phisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^{r}$ dynamical systems.stems.

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.577-594
• /
• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.345-351
• /
• 2005

An effective method for analyzing the stability of nonlinear systems is developed. After introducing a novel concept named the point- wise generalized Dahlquist constant for any mapping and presenting its useful properties, we show that the point-wise generalized Dahlquist constant is sufficient for characterizing the exponential stability of nonlinear systems.

• Journal of Korea Society of Industrial Information Systems
• /
• v.11 no.5
• /
• pp.62-66
• /
• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

• Communications of the Korean Mathematical Society
• /
• v.23 no.3
• /
• pp.357-369
• /
• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• Journal of applied mathematics & informatics
• /
• v.6 no.3
• /
• pp.929-935
• /
• 1999

By applications of the stability for a class of functional equa-tions we obtain the hyers-Ulam stability for the equations of the form g($\chi$+y)=kg($\chi$)g(y) in the following setting; ｜g($\chi$+y)-kg($\chi$)g(y)｜$\leq$$\Delta$($\chi$,y).

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.445-459
• /
• 2006

In this paper cellular neural networks with continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.