• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.2
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• pp.105-111
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• 2005

Though GF(2) CA can only handle data with bit units GF(2p) CA can handle data with units more than bit units. In this paper we analyze the state-transition of nongroup cellular automata(CA) with a single attractor over GF(2p). And we propose the constructing method the state-transition diagram of a linear SACA over GF(2p) by using the concept of basic path. Also we propose the state-transition diagram of the nonlinear complemented SACA by using the state-transition diagram of a linear SACA.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.113-121
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• 2002

We construct lots of non-self similar fractal sets called generalized Markov attractors for a given (hyperbolic) iterated function system and calculated bounds of their Hausdorff dimensions.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.465-472
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• 2015

In this paper, we study the existence and the stability of equilibria of predator-prey models with Ivlev's functional response. We give a simple proof for the uniqueness of limit cycles of the predator-prey system. The existence and the stability at the origin and a boundary equilibrium point(including the positive equilibrium point) are also investigated.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1241-1252
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• 2015

In this paper, we study the dynamical bifurcation of the modified Swift-Hohenberg equation on a periodic interval as the system control parameter crosses through a critical number. This critical number depends on the period. We show that there happens the pitchfork bifurcation under the spatially even periodic condition. We also prove that in the general periodic condition the equation bifurcates to an attractor which is homeomorphic to a circle and consists of steady states solutions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.2
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• pp.121-125
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• 2015

In this paper, we propose a method that extracts features from character patterns using the fractal dimension of chaos theory. The input character pattern image is converted into time-series data. Then, using the modified Henon system suggested in this paper, it determines the last features of the character pattern image after calculating the box-counting dimension, natural measure, information bit, and information (fractal) dimension. Finally, character pattern recognition is performed by statistically finding each information bit that shows the minimum difference compared with a normalized character pattern database.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.275-282
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• 2008

Our aim in this paper is to investigate the global attractivity of the recursive sequence $x_{n+1}$ = $\frac{\alpha-{\beta}x_{n-1}}{\gamma+g(x_n)}$ under specified conditions. We show that the positive (or zero for $\alpha$ = 0) equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients and the function g(x).

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.1
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• pp.71-81
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• 1997

This paper describes an implementation of Chua's oscillator circuits with five - segment piecewise -linear function. Some bifurcation phenomena and chaotic attractors observed experimentally from the laboratory model and simulated by computer for the model are also presented. The Chua's oscillator circuit is implemented with analog electronic devices. Com¬paring both the observations and simulations, the spectrums are satisfactory.

• Journal of KSNVE
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• v.7 no.3
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• pp.489-498
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• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1445-1465
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• 2015

In this paper, the long time behavior of the convective Cahn-Hilliard equation in two dimensions is considered, semidiscrete and completely discrete spectral approximations are constructed, error estimates of optimal order that hold uniformly on the unbounded time interval $0{\leq}t<{\infty}$ are obtained.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1039-1048
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• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.