• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.577-585
• /
• 2007

We introduce the inverse shadowing property of geometric Lorenz flows and prove that the geometric Lorenz flows do not have the inverse shadowing property.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.581-588
• /
• 2016

Komuro [3] proved that geometric Lorentz attractor does not satisfy the shadowing property. In this paper we study the condition under which geometric Lorenz attractor has the orbital shadowing property that is weaker than the shadowing property.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
• /
• v.28 no.4
• /
• pp.133-142
• /
• 2023

In this paper, we built a data-driven artificial intelligence model using RNN-LSTM (Recurrent Neural Networks-Long Short-Term Memory) to predict the Lorenz system, and examined the possibility of whether this model can replace chaotic dynamic models. We confirmed that the data-driven model reflects the chaotic nature of the Lorenz system, where a small error in the initial conditions produces fundamentally different results, and the system moves around two stable poles, repeating the transition process, the characteristic of "deterministic non-periodic flow", and simulates the bifurcation phenomenon. We also demonstrated the advantage of adjusting integration time intervals to reduce computational resources in data-driven models. Thus, we anticipate expanding the applicability of data-driven artificial intelligence models through future research on refining data-driven models and data assimilation techniques for data-driven models.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.50 no.2
• /
• pp.90-95
• /
• 2001

Electric arc furnaces (EAFs) has a process to cause the degradation of the electric power quality such as voltage flicker. In order to adequately understand and analyze the effects on the power system from these loads, obtaining an accurate representation of the characteristics of the loads is crucial. In this paper, a mixed chaotic EAF model to represent the low frequency and high frequency variations of the arc current respectively has been proposed. The Lorenz system may contribute to the low frequency components of arc current and the logistic equation may contribute to the high frequency components, and the proposed mixed model will be a combination of both Lorenz and logistic model. The concept of chaotic parameters, such as chaotic resistance, inductance of admittance has been also proposed for the characterization of arc furnace operation and the highly nonlinear physical processes. The power quality indices are calculated from the simulated waveforms and compared with the actual power quality indices statistics in order to illustrate the model's capabilities.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.14 no.4
• /
• pp.322-331
• /
• 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 Data and Information Science Society
• /
• v.25 no.4
• /
• pp.903-914
• /
• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• East Asian mathematical journal
• /
• v.37 no.5
• /
• pp.591-598
• /
• 2021

In this paper we study the Cauchy problem for the Chern-Simons gauged O(3) sigma model. We prove the local existence of solutions with low regularity initial data, observing null forms of the system and applying bilinear estimates for wave-Sobolev space H^{s, b}.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.2
• /
• pp.270-275
• /
• 2005

This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Doffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.

• The Korean Journal of Applied Statistics
• /
• v.23 no.4
• /
• pp.767-776
• /
• 2010

Frontier (1976) suggested a criterion based on the expected length of ordered random intervals under the Broken-stick model (Barton and David, 1956) to determine the optimal number of principal components retained. It is considered to be one of the methods that provide the most consistent simulation results (Jackson, 1993). This study is aimed to propose a method using the distribution of ordered random intervals to evaluate the contribution of principal components. We also examine several types of Gini indices along with the corresponding Lorenz curves to visualize the overall equivalence of those contributions.

• Journal of the Korean earth science society
• /
• v.36 no.7
• /
• pp.611-616
• /
• 2015

El Nino and Southern Oscillation (ENSO) presents a broad band (2-8 year) variability and slowly changing amplitude and period, which are respectively referred to as ENSO irregularity and ENSO modulation. In this study, we developed a nonlinear low-order climate model by combining the Lorenz-63 model of nonlinear atmospheric variability and a simple ENSO model with recharge oscillator characteristics. The model successfully reproduced the ENSO-like variations in the sea surface temperature of eastern Pacific, such as the peak period, wide periodicity, and decadal modulations. The results show that the chaotic atmospheric forcing can lead to ENSO irregularity and ENSO modulation. It is also suggested the high probability of La Nina development could be associated with strong convection of the western warm pool. Although it is simple, this model is expected to be used in research on long-term climate change because it well captures the nonlinear air-sea interactions in the equatorial Pacific.