• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.105-116
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• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.53-63
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• 2000

The inverse shadowing property of a dynamical system is an "inverse" form of the shadowing property of the system. Recently, Kloeden and Ombach proved that if an expansive system on a compact manifold has the shadowing property then it has the inverse shadowing property. In this paper, we study topological stability of the inverse shadowing dynamical systems. In particular, we show that if an expansive system on a compact manifold has the inverse shadowing property then it is topologically stable, and so it has the shadowing property.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.687-690
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• 1991

In deterministic design of feedback controllers for uncertain dynamical systems, the bound on the uncertainty is an important clue to guarantee the asymptotic stability or uniform ultimate boundedness of the closed-loop system. In this paper, using only the measurable output we propose an adaptation law for the estimation of the bound of the uncertainty. And based on this adaptation law an adaptive control which renders the uncertain dynamical systems uniformly ultimately bounded is constructed.

• Journal of Korea Multimedia Society
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• v.4 no.2
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• pp.182-188
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• 2001

In this paper, We proposed a pseudo-random bit sequence generator based on the concept of n-dimensional cellular automata which is a method of analyzing dynamical systems. The proposed generator is designed for using and disusing key. And the key size is variable from 128 bits to 256 bits. The generator was estimated to generate 380Mbits/sec under Pentium MMX 200MHz (64M RAM, Windows 98).

• Journal of Korea Multimedia Society
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• v.8 no.5
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• pp.670-678
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• 2005

A Cellular Automaton(CA) is a dynamical system in which space and time are discrete, the state of each cell is unite and is updated by local interaction. Since the characteristics of CA is diffusion and local interaction, CA is used by crypto-systems and VLSI structure. In this study, we proposed a hash function based on the concept of 2-dimensional cellular automata and analyzed the proposed hash function.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.667-669
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• 1995

This paper presents a method to design Kalman filter on continuous stochastic dynamical systems via BPFT(block pulse functions transformation). When we design Kalman filter, minimum error valiance matrix is appeared as a form of nonlinear matrix differential equations. Such equations are very difficult to obtain the solutions. Therefore, in this paper, we simply obtain the solutions of nonlinear matrix differential equations from recursive algebraic equations using BPFT. We believe that the presented method is very attractive and proper for the evaluation of Kalman gain on continuous stochastic dynamical systems.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.1021-1024
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• 2000

In this paper, a neuro-fuzzy system for quantitative characterization of chaotic signals is proposed. The proposed system is differ from the previous methods in that the nonlinear functions of the nonlinear dynamical systems are calculated as the invariant factor. In the proposed neuro-fuzzy system, the nonlinear functions are determined by supervised learning. From the reconstructed nonlinear functions, the proposed system can generate extrapolated chaotic signals. This feature will help the study of nonlinear dynamical systems which require large number of chaotic data. To confirm the validity of the proposed system, nonlinear functions are reconstructed from 1-dimensional and 2-dimensional chaotic signals.

• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.4
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• pp.67-76
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• 1995

In recent research on the fuzzy controller, the crisp type fuzzy controller model, in which the consequent part of the fuzzy control rules are crisp real numbers instead of fuzzy sets, due to its simplicity in calculation, has been widely used in various applications. In this paper we try to analyze the dynamical behavior of the crisp type fuzzy controller with both inference methods of min-max compositional rule and product-sum inference. The analysis reveals that a crisp type fuzzy controller behaves approximately like a PD controller.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.869-878
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• 2013

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.

• The Bulletin of The Korean Astronomical Society
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• v.30 no.2
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• pp.75.1-75.1
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• 2005