• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.779-793
• /
• 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.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.51 no.5
• /
• pp.44-50
• /
• 2014

Chaos communication system is one of the security algorithms that is applied to improve the security. Chaos signal is non-linear, and it is generated randomly according to the initial conditions. Also, chaos communication system has characteristics such as non-periodic, wide-band, non-predictability of signals and easy implementation. So, security of chaos communication system is superior, and it has low interception probability and good anti-jamming characteristic. However, BER performance is worse than digital communication system, because it has many self interference signal in case of CDSK system. To improve these disadvantages, we analyze the PDF trend which can improve the BER performance in existing study, and we proposed a chaos map. And, proposed chaos map was defined as the 'Boss map'. Generally, BER performance is changed according to initial values, parameters and spreading factors. Therefore, in this paper, we will introduce PDF trends which can improve the BER performance, and will describe about Boss map. Also, characteristics of Boss map is analyzed by evaluating the BER performance of Boss map according to initial values, parameters and spreading factors. As a result, while maintaining the similar BER performance, initial value of Boss map can be selected from 0 to 1.2, and BER performance is best when parameter alpha is 2.5. Also, BER performance is best when spreading factor is 50.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.498-504
• /
• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1996.10a
• /
• pp.295-300
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.451-458
• /
• 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
• /
• 1993.10a
• /
• pp.1234-1239
• /
• 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.

• Proceedings of the IEEK Conference
• /
• 2002.07b
• /
• pp.794-797
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.2 no.2
• /
• pp.157-162
• /
• 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)

• Journal of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.71-90
• /
• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.799-804
• /
• 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.