• 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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.327-335
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• 2004

In this paper, we reformulate a snapshot attractor([5]), ($K,\;\={\mu_{\iota}}$) generated by a random baker's map with a sequence of probability measures {\={\mu_{\iota}}} on K. We obtain bounds of the correlation dimensions of ($K,\;\={\mu_{\iota}}$) for all ${\iota}\;{\geq}\;1$.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.165-171
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• 2014

Let M be a manifold with a volume form ${\omega}$ and $f:M{\rightarrow}M$ be a diffeomorphism of class 𝒞$^1$ that preserves ${\omega}$. We prove that if M is almost bounded for the diffeomorphism f, then M is chain recurrent. Moreover, we get that Lagrange stable volume-preserving manifolds are also chain recurrent.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2000.05a
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• pp.247-254
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• 2000

Chua's circuit is a simple electronic network which exhibits a variety of bifurcation and attractors. The circuit consists of two capacitors, an inductor, a linear resistor, and a nonlinear resistor. In this paper, a transmitter and a receiver using two identical Chua's circuits are proposed and a synchronizations methods are investigated. Since the synchronization of the transmission system or nonidea system are impossible by coupled synchronization, the drive-response synchronization theory were used.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.73-80
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• 2009

This paper aims to study local and global structure of holomorphic flows on $\mathbb{C}^1$. At a singular point of a holomorphic flow, we locally sector the flow into parabolic or elliptic types. By the local structure of holomorphic flows, we classify all the possible types of topologies of $\omega$-limit sets.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.97-106
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• 2012

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.357-378
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• 2012

In this paper, we consider the convective Cahn-Hilliard equation. Based on the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in $H^k$($k\geq0$) space, which attracts any bounded subset of $H^k({\Omega})$ in the $H^k$-norm.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.187-190
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• 2000

Chua's circuit is a simple electronic network which exhibits a variety of bifurcation and attractors. The circuit consists of two capacitors, an inductor, a linear resistor, and a nonlinear resistor. In this paper, a transmitter and a receiver using two identical Chua's circuits are proposed and synchronizations of a power line are investigated. Since the synchronization of the power line system is impossible by coupled synchronization, theory having both the drive-response and the coupled synchronization is proposed. As a result, the chaos synchronization has delay characteristics in the power line transmission system caused by the line parameters L and C.

• Proceedings of the KIEE Conference
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• 1998.07g
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• pp.2272-2274
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• 1998

This paper presents recognition and classification of high impedance fault(HIF) patterns in the electrical power systems based on chaotic features. Chaotic features are obtained from two dimensional chaos attractors reconstructed from fault current waveform. The RBFN is trained with the two types of HIF data generated by the electromagnetic transient program and measured from actual faults. The RBFN successfully classifies normal and the three types of fault patterns based on the binary chaotic features.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2404-2406
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• 2000

Chua's circuit is a simple electronic network which exhibits a variety of bifurcation and attractors. The circuit consists of two capacitors, an inductor, a linear resistor, and a nonlinear resistor. In this paper, a transmitter and a receiver using two identical Chua's circuits are proposed and synchronizations of a T or ${\pi}$ type power line are investigated. Since the synchronization of the power line system is impossible by coupled synchronization, theory having both the drive-response and the coupled synchronization is proposed. As a result, the chaos synchronization has delay characteristics in the power line transmission system caused by the line parameters L and C