• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.779-793
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• 2009

This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.

• 전자공학회논문지
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• 제51권5호
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• pp.44-50
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• 2014

카오스 통신 시스템은 보안성을 향상시키기 위해 적용하는 보안 알고리즘 중에 하나이다. 카오스 신호는 비선형적이며 초기조건에 따라 불규칙하게 생성된다. 또한, 카오스 통신 시스템은 비주기성, 광대역성, 비예측성, 구현의 용이성 등의 특성을 가지고 있다. 그래서 카오스 통신 시스템은 보안성이 우수하고 낮은 도청 확률과 좋은 항재밍 특성을 갖는다. 하지만 BER 성능은 디지털 통신 시스템보다 나쁘게 평가되는데, CDSK 방식의 경우에는 많은 자기 간섭 신호로 인해 BER 성능이 열화된다. 이런 단점을 개선하기 위해, 우리는 이전 연구에서 BER 성능을 향상시킬 수 있는 PDF 경향을 분석하고 이를 통해 카오스 맵을 제안하였다. 그리고 제안한 카오스 맵은 Boss map이라고 정의하였다. 일반적으로, 카오스 맵의 초기값과 매개변수, 확산인자에 따라 BER 성능이 달라진다. 따라서, 본 논문에서는 BER 성능을 향상시킬 수 있는 PDF 경향을 소개하고, Boss map에 대해 설명한다. 또한, Boss map의 초기값과 매개변수, 확산인자에 따른 BER 성능을 평가하여 Boss map의 특성을 분석한다. 그 결과, Boss map은 유사한 BER 성능을 유지하면서 초기값을 0부터 1.2까지 선택할 수 있으며, 매개변수 알파값은 2.5일 때 가장 좋은 BER 성능을 보인다. 또한, 확산인자 값이 50일 때 가장 좋은 BER 성능을 가진다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.498-504
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• 2002

Vibration beat phenomenon is theoretically investigated on a slightly asymmetric cylindrical shell, which is a simplified model of Korean bell. Mode pairs of the slightly asymmetric shell are obtained by receptance analysis and impulse response of the shell is derived using modal expansion and Laplace transform. Based on the impulse response model, beat mapping method is proposed to explain the reason that the beat of a bell vibration shows periodic distribution on the circumference. Beat characteristics of King Song-Dok Bell are explained in detail using the beat map and the measured modal data.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 추계학술대회논문집; 한국과학기술회관, 8 Nov. 1996
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• pp.295-300
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• 1996

In this study, the dynamic instabilities of a nonlinear elastic system subjected to follower force are investigated. The two-degree-of-freedom double pendulum model with nonlinear geometry, cubic spring, and linear viscous damping is used for the study. The constant and periodic follower forces are considered. The chaotic nature of the system is identified using the standard methods, such as time histories, phase portraits, and Poincare maps, etc.. The responses are chaotic and unpredictable due to the sensitivity to initial conditions. The sensitivities to parameters, such as geometric initial imperfections, magnitude of follower force, and viscous damping, etc. is analysed. The strange attractors in Poincare map have the self-similar fractal geometry. Dynamic buckling loads are computed for various parameters, where the loads are changed drastically for the small change of parameters.

• 대한수학회논문집
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• 제24권3호
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• pp.451-458
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• 2009

The set of root classes plays a crucial role in the Nielsen root theory. Extending Brown et al.'s work on the set of root classes of iterates of maps, we rearrange it into the reduced orbit set and show that under suitable hypotheses, any reduced orbit has the full depth property as in the Nielsen type theory of periodic orbits.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.1234-1239
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• 1993

We study how to design conventional feedback controllers to drive chaotic trajectories of the well-known systems to their equilibrium points or any of their inherent periodic orbits. The well-known chaotic systems are Heon map and Duffing's equation, which are used as illustrative examples. The proposed feedback controller forces the chaotic trajectory to the stable manifold as OGY method does. Simulation results are presented to show the effectiveness of the proposed design method.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -2
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• pp.794-797
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• 2002

We consider a master-slave pulse-coupled network of bifurcating integrate-and-fire circuits. The network exhibits in-phase chaotic synchronization and various periodic synchronization phenomena. In order to analyze these phenomena precisely, we derive a one-dimensional return map. Also using a simple test circuit, typical phenomena are demonstrated in the laboratory.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.157-162
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• 1995

Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)

• 대한수학회지
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• 제60권1호
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• pp.71-90
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• 2023

We construct generalized Cauchy-Riemann equations of the first order for a pair of two ℝ-valued functions to deform a minimal graph in ℝ³ to the one parameter family of the two dimensional minimal graphs in ℝ⁴. We construct the two parameter family of minimal graphs in ℝ⁴, which include catenoids, helicoids, planes in ℝ³, and complex logarithmic graphs in ℂ². We present higher codimensional generalizations of Scherk's periodic minimal surfaces.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.799-804
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• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.