• 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.

• Journal of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.473-493
• /
• 2014

This paper concerns with a class of delayed Nicholson's blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.

• The Pure and Applied Mathematics
• /
• v.5 no.1
• /
• pp.13-16
• /
• 1998

For continuous maps f of the circle to itself, we show that (1) every $\omega$-limit point is recurrent (or almost periodic) if and only if every $\omega$-limit set is minimal, (2) every $\omega$-limit set is almost periodic, then every $\omega$-limit set contains only one minimal set.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.873-887
• /
• 2007

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.1
• /
• pp.39-52
• /
• 2022

We introduce Clifford-valued neural networks with leakage delays. Furthermore, we study the uniqueness and existence of Clifford-valued Hopfield artificial neural networks having the Stepanov weighted pseudo almost periodic forcing terms on leakage delay terms. However the noncommutativity of the Clifford numbers' multiplication made our investigation diffcult, so our results are obtained by decomposing Clifford-valued neural networks into real-valued neural networks. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.635-644
• /
• 2010

We investigate the boundedness and asymptotic almost periodicity of solutions for discrete Volterra equations.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.707-720
• /
• 2000

Conley index is used study bifurcation from equilibria of full bounded solutions to parameter dependent families of ordinary differential equations of the form {{{{ {dx} over {dt} }}}} =$\varepsilon$F(x, t, $\mu$). It is assumed that F(x, t,$\mu$) is uniformly almost periodic in t.

• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• pp.235-239
• /
• 2005

In this paper we study some characterizations of proximal, distal and almost one to one homomorphisms of flows. In particular we show that if the almost one to one proximal extension of a minimal flow is weakly almost periodic, then it is minimal.

• Korean Journal of Mathematics
• /
• v.8 no.1
• /
• pp.27-32
• /
• 2000

In this paper, we show that for any continuous map $f$ of the circle $S^1$ to itself, (1) $x{\in}{\Omega}(f){\backslash}\overline{R(f)}$, then $x$ is not a turning point of $f$ and (2) if $P(f)$ is non-empty, then $R(f)$ is closed if and only if $AP(f)$ is closed.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.49-58
• /
• 2016

We study the existence of S-asymptotically ${\omega}$-periodic mild solutions of partial functional integrodifferential equation by the method of Caicedo et al. [2].