• 대한수학회보
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• 제46권6호
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• pp.1237-1248
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• 2009

The domain of attraction of a nonlinear differential equations is the region of initial points of solution tending to the equilibrium points of the systems as the time going. Determining the domain of attraction is one of the most important problems to investigate nonlinear dynamical systems. In this article, we first present two algorithms to determine the domain of attraction by using the moment matrices. In addition, as an application we consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method, and also estimate the domain of attraction by using the algorithms.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.349-358
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• 2018

In this article, we discuss the domain of attraction of HIV-1 system by using the moment theory. First, the asymptotic stabilities of the equilibrium point of the system are given, and then we introduce how to use the moment method to estimate domain of attraction. Finally, one simulation shows the effectiveness of moment method.

• 대한수학회지
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• 제54권3호
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• pp.1049-1061
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• 2017

The paper presents a characterization of stable random measures, giving a canonical form of their Laplace transform. Domain of attraction of stable random measures is concerned in a theorem showing that a random measure belongs to domain of attraction of any stable random measures if and only if it varies regularly at infinity.

• 대한수학회보
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• 제49권3호
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• pp.517-528
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• 2012

This paper is estimating the domain of attraction for a class of susceptible-exposed-infectious-recovered (SEIR) epidemic dynamic models by using sum of squares optimization. First, the stability is analyzed for the equilibriums of SEIR model, and the domain of attraction in the endemic equilibrium is estimated by using sum of squares optimization. Finally, a numerical example is examined.

• 대한기계학회논문집A
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• 제24권1호
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• pp.240-249
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• 2000

An improved global optimization algorithm is developed by extending the domain elimination method. The concept of triangular patch consists of two or more trajectories of local minimizations is introduced to widen the attraction region of the domain elimination method. Using the an-]c between each of three vertices of the patch and a design point, we measure the proximity, between the design point and the patch. With the Gram-Schimidt orthonormalization, this method can be extended to general n-dimensional problems. We code the original domain elimination algorithm and a patch-based algorithm. Then we compare the performance of two algorithms. Through the well-known example problems. the algorithm using patch is shown to be superior to the original domain elimination algorithm in view of computational efficiency.

• Journal of the Korean Statistical Society
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• 제25권3호
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• pp.313-336
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• 1996

In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.43.5-43
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• 2001

This paper considers a new synthesis of the optimally performing brain-state-in-a-box (BSB) neural associative memory given a set of prototype patterns to be stored as asymptotically stable equilibrium points with the large and uniform size of the domain of attraction (DOA). First, we propose a new theorem that will be used to provide a guideline in design of the BSB neural associative memory. Finally, a design example is given to illustrate the proposed approach and to compare with existing synthesis methods.

• 대한기계학회논문집
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• 제16권9호
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• pp.1711-1721
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• 1992

본 연구에서는 Nayfeh등과 이원경과 소강영은 조화가진하의 핀과 꺽쇠로 고정 된 보(hinged-clamped beam)의 강제 진동 해석을 통하여 점근적으로 안정한 정상상태 응답이 둘 이상 존재할 수 있음을 알게 되었다. 본 연구에서는 이 경우에 접근적으 로 안정한두 정상상태 응답을 구하고 이들 안정한 해로 각각 흡인되는 초기조건들의 집합인 흡인영역을 보간사상법(interpolated mapping method)과 직접 수치적분에 의해 구한 후 서로 비교하였다.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.289-297
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• 1997

It is well known that the spacings, the differences of two successive order statistics, in a random sample of size n from a distribution function F are independent and exponentially distributed if F is itself the exponential distribution. In this paper we obtain an asymptotically similar result on a fixed number of upper spacings as n .to. .infty. for a general F under the assumption that F is in the domain of attraction of some extreme value distribution. For a heavy or short tailed F, appropriate log transformations of the sample should be proceded to get the result. As a by-product, we also get that each upper spacing diverges in probability to .infty. and converges in probability to 0 as n .to. .infty. for a heavy and short tailed F, respectively, which is fully expected.

• 대한수학회보
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• 제48권6호
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.