• 대한수학회지
• /
• 제37권5호
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제31권3_4호
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제49권2호
• /
• pp.299-312
• /
• 2009

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with nonautonomous N-dimensional impulsive Lotka Volterra competitive systems with dispersions and fixed moments of impulsive perturbations. By using the techniques of piecewise continuous Lyapunov's functions new sufficient conditions for the global exponential stability of the unique almost periodic solutions of these systems are given.

• 충청수학회지
• /
• 제34권3호
• /
• pp.221-234
• /
• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• 충청수학회지
• /
• 제23권4호
• /
• pp.635-644
• /
• 2010

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

• Journal of applied mathematics & informatics
• /
• 제31권1_2호
• /
• pp.247-262
• /
• 2013

In this paper, using the time scale calculus theory, we first discuss the permanence of a $n$-species competition system with feedback control on time scales. Based on the permanence result, by the Lyapunov functional method, we establish sufficient conditions for the existence and uniformly asymptotical stability of almost periodic solutions of the considered model. The results of this paper is completely new. An example is employed to show the feasibility of our main result.

• 충청수학회지
• /
• 제35권1호
• /
• 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.

• 대한수학회논문집
• /
• 제32권2호
• /
• pp.457-466
• /
• 2017

We study the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some partial functional integrodifferential equations with infinite delay and nonlocal conditions.

• Korean Journal of Mathematics
• /
• 제30권3호
• /
• pp.491-502
• /
• 2022

In this paper we investigate some sufficient conditions to guarantee the existence and uniqueness of Stepanov-like weighted pseudo almost periodic solutions of cellular neural networks on Clifford algebra for non-automomous cellular neural networks with multi-proportional delays. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• 충청수학회지
• /
• 제29권1호
• /
• 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].