• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.857-870
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• 2000

In this paper, we estimate correlation dimensions of discrete quasi periodic ordits with frequencies, irrational numbers, which are called quasi Roth numbers. We specify the lower estimate valuse of the dimensions by using the parameters which are derived the rational approximable properties of the quasi Roth numbers.

• Journal of computational fluids engineering
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• v.16 no.3
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• pp.52-58
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• 2011

This study investigates the bifurcation sequence to chaos in a horizontal annulus with a constant heat flux wall. After the first Hopf bifurcation from a steady to a simple time-periodic flow with a fundamental frequency, quasi-periodic flows with two or three incommensurable frequencies appear. A reverse transition from a quasi-periodic flow to a simple periodic flow is observed with increase of Rayleigh number. And finally, chaotic convection is established after appearance of three incommensurable frequencies at a high Rayleigh number. Simple periodic flows exist between quasi periodic flows. The transition route to chaos of the present simulations follows the Ruelle-Takens route.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1223-1240
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• 2012

The system $$\dot{x}=(A+{\varepsilon}Q(t,{\varepsilon}))x+{\varepsilon}g(t,{\varepsilon})+h(x,t,{\varepsilon}),$$ where A is elliptic whose eigenvalues are not necessarily simple and $h$ is $\mathcal{O}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.3
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• pp.433-441
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• 2001

Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1107-1120
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• 2024

In this note, we investigate new types of p-adic Dedekind sums. They interpolate the Apostol-Dedekind sum associated with quasi-periodic Euler functions in different ways. We also obtain the integral representation and a reciprocity relation, respectively.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1229-1254
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• 2022

In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for ℤ^d₊-actions, explore the connections of levels of the topological structure the orbits of (quasi-)weakly almost periodic points and discuss the relations between (quasi-)weakly almost periodic point and minimal center of attraction. Especially, we investigate the chaotic dynamics near or inside the minimal center of attraction of a point in the cases of S-generic setting and non S-generic setting, respectively. Actually, we show that weakly almost periodic points and quasi-weakly almost periodic points have distinct topological structures of the orbits and we prove that if the minimal center of attraction of a point is non S-generic, then there exist certain Li-Yorke chaotic properties inside the involved minimal center of attraction and sensitivity near the involved minimal center of attraction; if the minimal center of attraction of a point is S-generic, then there exist stronger Li-Yorke chaotic (Auslander-Yorke chaotic) dynamics and sensitivity (ℵ₀-sensitivity) in the involved minimal center of attraction.

• ETRI Journal
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• v.26 no.3
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• pp.277-280
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• 2004

The distributions of electric field and induced second-order nonlinearity are analyzed in the periodic poling of optical fibers. A quasi-phase matching efficiency for the induced nonlinearity is calculated in terms of both the electrode separation distance between the applied voltage and generalized electrode width for the periodic poling. Our analysis of the quasi-phase matching efficiency implies that the conversion efficiency can be enhanced through adjusting the separation distance, and the electrode width can be maximized if the electrode width is optimized.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.4
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• pp.322-331
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• 2014

Chaotic dynamics is an active area of research in biology, physics, sociology, psychology, physiology, and engineering. This interest in chaos is also expanding to the social scientific fields such as politics, economics, and argument of prediction of societal events. In this paper, we propose a dynamic model for addiction of tobacco. A proposed dynamical model originates from the dynamics of tobacco use, recovery, and relapse. In order to make an addiction model of tobacco, we try to modify and rescale the existing tobacco and Lorenz models. Using these models, we can derive a new tobacco addiction model. Finally, we obtain periodic motion, quasi-periodic motion, quasi-chaotic motion, and chaotic motion from the addiction model of tobacco that we established. We say that periodic motion and quasi-periodic motion are related to the pre-addiction or recovery stage, respectively. Quasi-chaotic and chaotic motion are related to the addiction stage and relapse stage, respectively.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.39-52
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• 2019

The aim of this paper is to introduce the notions of (quasi) weakly almost periodic point, measure center and minimal center of attraction of amenable group actions, explore the connections of levels of the orbit's topological structure of (quasi) weakly almost periodic points and study chaotic dynamics of transitive systems with full measure centers. Actually, we showed that weakly almost periodic points and quasiweakly almost periodic points have distinct orbit's topological structure and proved that there exists at least countable Li-Yorke pairs if the system contains a proper (quasi) weakly almost periodic point and that a transitive but not minimal system with a full measure center is strongly ergodically chaotic.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.710-711
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• 2014

In many cases, periodic noise occurs because most applications include motors, compressors and so on which have reciprocating motion. The noise usually contains tones at the fundamental frequency and at several higher harmonic frequencies in practice. For this type of noise, we developed a frequency-domain active noise control algorithm and determined that it's effective. However, the performance deteriorated for quasi-periodic noise. In this paper, we develop compensated frequency-domain active noise control algorithm for quasi-periodicity. And then, we implement computer simulation and compare the performance.