• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.17-39
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• 2013

The study of nonlinear discrete-time control dynamical systems with disturbance is an important topic in control theory. In this paper, we concentrate our efforts to multiple valued iterative dynamical systems, which model the nonlinear discrete-time control dynamical systems with disturbance. After establishing the validity of such modeling, we study the invariant set theory of the multiple valued iterative dynamical systems, including the controllability/reachablity problems of the maximal invariant sets.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.703-713
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• 2012

In this paper we study ${\omega}$-limit sets and attraction of non-autonomous discrete dynamical systems. We introduce some basic concepts such as ${\omega}$-limit set and attraction for non-autonomous discrete system. We study fundamental properties of ${\omega}$-limit sets and discuss the relationship between ${\omega}$-limit sets and attraction for non-autonomous discrete dynamical systems.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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• pp.341-355
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• 2017

This paper is devoted to some dynamical properties such as transitivity, mixing and specification of two discrete dynamical systems (X, f) and ($2^X$, ${\bar{f}}$) on compact metric spaces.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.155-163
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• 2002

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.397-406
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• 1997

In this paper we introduce GESS method and show that dynamics of the system ｙ＇=A(s,t,y) ｙ is more faithfully approxi-mated by GESS method that by Euler method. Numerical experiments are given for the comparison of GESS method with Euler method.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.157-172
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• 1998

A numerical method is proposed for dynamical systems. We utilize the fact that special matrix exponentials can be exactly evaluated by the intrinsic library functions. Numerical examples are given, which show that the relative error s of the proposed method converge to a small constant and that the method faithfully approximates the dynamics of the nonlinear differential equations.

• East Asian mathematical journal
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• v.27 no.5
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• pp.521-525
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• 2011

We use a weaker version of the celebrated Newton-Kantorovich theorem [3] reported by us in [1] to find solutions of discrete dynamical systems involving operators with chaotic behavior. Our results are obtained by extending the application of the shadowing lemma [4], and are given under the same computational cost as before [4]-[6].

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.4
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• pp.574-581
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• 1996

The neural network approach has been shown to be a general scheme for nonlinear dynamical system identification. Unfortunately the error surface of a Multilayer Neural Networks(MNN) that widely used is often highly complex. This is a disadvantage and potential traps may exist in the identification procedure. The objective of this paper is to identify a nonlinear dynamical systems based on Self-Organized Distributed Networks (SODN). The learning with the SODN is fast and precise. Such properties are caused from the local learning mechanism. Each local network learns only data in a subregion. This paper also discusses neural network as identifier of nonlinear dynamical systems. The structure of nonlinear system identification employs series-parallel model. The identification procedure is based on a discrete-time formulation. Through extensive simulation, SODN is shown to be effective for identification of nonlinear dynamical systems. (author). 13 refs., 7 figs., 2 tabs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.87-93
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• 2004

The E-Euler process has been proposed for autonomous dynamical systems in [7]. In this paper, the E-Euler process is extended to nonautonomous dynamical systems. When a discrete function is bounded or gradually decreases to ${\epsilon}\;<<\;1$ as $n\;{\rightarrow}\;{\infty}$, it is shown that the relative error converges to a constant or decreases.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.46-51
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• 1987

Using the computer-generated Lyapunov functions due to Brayton-tong's constructive algorithm, we estimate the domains of attraction of dynamical systems of the second order, and analyze the asymptotic stability of large scale contincous-time and discrete-time systems by the decomposition and aggregation method. With this approach we get the less conservative stability results than the existing methods.