• The Journal of the Korea institute of electronic communication sciences
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• v.5 no.2
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• pp.158-163
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• 2010

In this paper, we implemened the simplified Chua's circuit which is replace L to C by real hardware implementation. Because L element has a difficult problem to make a real hardware, L has a saturation characteristic and we also compare with previous Chua's circuit as the result of chaostic attractors creation.

• Speech Sciences
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• v.8 no.3
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• pp.149-157
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• 2001

Based on the chaos theory, a new method of presentation of speech signal has been presented in this paper. This new method can be used for pattern matching such as speaker recognition. The expressions of attractors are represented very well by the logistic maps that show the chaos phenomena. In the speaker recognition field, a speaker's vocal habit could be a very important matching parameter. The attractor configuration using change value of speech signal can be utilized to analyze the influence of voice undulations at a point on the vocal loudness scale to the next point. The attractors arranged by the method could be used in research fields of speech recognition because the attractors also contain unique information for each speaker.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.583-605
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• 2024

This paper discusses the properties of attractors of Type 1 IFS which construct self similar fractals on product spaces. General results like continuity theorem and Collage theorem for Type 1 IFS are established. An algebraic equivalent condition for the open set condition is studied to characterize the points outside a feasible open set. Connectedness properties of Type 1 IFS are mainly discussed. Equivalence condition for connectedness, arc wise connectedness and locally connectedness of a Type 1 IFS is established. A relation connecting separation properties and topological properties of Type 1 IFS attractors is studied using a generalized address system in product spaces. A construction of 3D fractal images is proposed as an application of the Type 1 IFS theory.

• 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.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.519-532
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• 2016

We consider the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations with infinite delays. We prove the existence of a pullback $\mathcal{D}$-attractor for the continuous process associated to the problem with respect to a large class of non-autonomous forcing terms.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.411-417
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• 2007

In this paper, the connection among the attractor, the attractor neighborhood and the domain of influence are investigated. A necessary and sufficient condition of the existence of the quasi-attractor is established. Some results of Conley in [2] are generalized.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.583-599
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• 2018

In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

• Journal of KIISE:Computer Systems and Theory
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• v.37 no.3
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• pp.138-146
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• 2010

It is well known that many biological networks are very robust against various types of perturbations, but we still do not know the mechanism of robustness. In this paper, we find that there exist a number of feedback loops in a real biological network compared to randomly generated networks. Moreover, we investigate how the topological property affects network robustness. To this end, we properly define the notion of robustness based on a Boolean network model. Through extensive simulations, we show that the Boolean networks create a nearly constant number of fixed-point attractors, while they create a smaller number of limit-cycle attractors as they contain a larger number of feedback loops. In addition, we elucidate that a considerably large basin of a fixed-point attractor is generated in the networks with a large number of feedback loops. All these results imply that the existence of a large number of feedback loops in biological networks can be a critical factor for their robust behaviors.

• Korean Journal of Mathematics
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• v.3 no.2
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• pp.315-318
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• 1995