• 충청수학회지
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• 제24권1호
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• pp.105-112
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• 2011

In this paper, we investigate h-stability of the nonlinear perturbed difference system by using comparison principle.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.489-496
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• 2004

We study the h- stability of nonlinear difference system x(n+1) =f(n, x(n)) and its perturbed system y(n+l) =f(n, y(n))+g(n, y(n), Sy(n)).

• 전기학회논문지
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• 제59권6호
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• pp.1159-1166
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• 2010

To improve prediction quality of a nonlinear prediction system, the system's capability for uncertainty of nonlinear data should be satisfactory. This paper presents a TSK fuzzy prediction system that can consider and deal with the uncertainty of nonlinear data sufficiently. In the design procedures of the proposed system, HCBKA(Hierarchical Correlationship-Based K-means clustering Algorithm) was used to generate the accurate fuzzy rule base that can control output according to input efficiently, and the first-order difference method was applied to reflect various characteristics of the nonlinear data. Also, multiple prediction systems were designed to analyze the prediction tendencies of each difference data generated by the difference method. In addition, to enhance the prediction quality of the proposed system, an error compensation method was proposed and it compensated the prediction error of the systems suitably. Finally, the prediction performance of the proposed system was verified by simulating two typical time series examples.

• 충청수학회지
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• 제24권4호
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• pp.883-893
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• 2011

In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

• 대한수학회논문집
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• 제20권2호
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• pp.351-358
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• 2005

We study asymptotic equivalence between nonlinear difference system $$\Delta\chi(n)=f(n,\chi(n))$$ and its variational system $${\Delta}v(n)=f_{\chi}(n,0)v(n)$$.

• 대한수학회보
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• 제44권1호
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• pp.177-184
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• 2007

We study the asymptotic behavior of nonlinear Volterra difference system $$x(n+1)=f(n,x(n))+{\sum\limits^{n}_{s=n_{o}}\;g(n,s,x(s)),\;x(n_{o})=xo$$ by using the resolvent matrix R(n, m) of the corresponding linear Volterra system and the comparison principle.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.683-691
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• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• 대한수학회보
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• 제38권1호
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• pp.101-111
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• 2001

We investigate the property of h-stability, which is an important extension of the notions of exponential stability and uniform Lipschitz stability in variation for nonlinear Volterra difference systems.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.277-284
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• 2013

In this paper, we investigate $h$-stability of the nonlinear perturbed difference system via $n_{\infty}$-similarity.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.491-504
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• 2018

In this article, we consider a fourth order nonlinear difference system. By making use of the critical point theory, we obtain some new existence theorems of at least one periodic solution with minimal period. Our main approach used in this article is the variational technique and the Saddle Point Theorem.