• The Journal of Natural Sciences
• /
• v.9 no.1
• /
• pp.75-81
• /
• 1997

The method of synchronization by feedbacking a signal of master system to a corresponding variable of slave system is applied to the Lorenz which is autonomous system. The two Lorenz systems are synchronized and the synchronization occurs when the consisting of the variable differences of the two systems generates infinite period of laminar phase. The characteristics of synchronization is analyzed in time series and phase spaces.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.7
• /
• pp.16-23
• /
• 2018

Chaos is one of the most significant topics in nonlinear science, and has been intensively studied since the Lorenz system was introduced. One characteristic of a chaotic system is that the signals produced by it do not synchronize with any other system. It therefore seems impossible for two chaotic systems to synchronize with each other, but if the two systems exchange information in just the right way, they can synchronize. This paper addresses the problem of synchronization in a modified Lorenz chaotic system based on active control, sliding mode control, and the Lyapunov stability theory. The considered synchronization scheme consists of identical drive and response generalized systems coupled with linear state error variables. For this, a brief overview of the modified Lorenz chaotic system is given. Then, control rules are derived for chaos synchronization via active control and slide mode control theory, with a strategy for solving the chattering problem. The asymptotic stability of the overall feedback system is established using the Lyapunov stability theory. A set of computer simulation works is presented graphically to confirm the validity of the proposed method.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.3
• /
• pp.143-148
• /
• 2011

In this paper, a backstepping design is proposed to achieve stabilization and synchronization for the Lorenz-Stenflo (LS) chaotic system. The proposed method is a recursive Lyapunov-based scheme and provides a systematic procedure to design stabilizing controllers. The proposed controller enables stabilization of the chaotic motion and synchronization of two identical LS chaotic systems using only a single control input. Numerical simulations are presented to validate the proposed method.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.4
• /
• pp.733-742
• /
• 2017

There are many areas of applications where Gumbel distribution are employed such as environmental sciences, system reliability and hydrology. The goodness-of-fit test for Gumbel distribution is very important in environmental sciences, system reliability and hydrology data analysis. Therefore, we propose the two test statistics to test goodness-of-fit for the Gumbel distribution based on the generalized Lorenz curve. We compare the new test statistic with the Anderson - Darling test, Cramer - vonMises test, and modified Anderson - Darling test in terms of the power of the test through by Monte Carlo method. As a result, the new test statistics are more powerful than the other test statistics. Also, we propose new graphic method to goodness-of-fit test for the Gumbel distribution based on the generalized Lorenz curve.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.22 no.11
• /
• pp.2488-2497
• /
• 1997

In this paper, a computer simulation of the Lornz discrete chaotic system is described. The chotic behavior closely matches the results predicted by numerical simulations. Using the concept of discrete synchronized chaotic systems, the possibility of a secure communication is proved by simulating the Lorenz system in both the transmitter and receiver. In the proposed approach, at first, a chaotic modulating signal is multiplied with the message, and these are transmitted with adding a chaotic modulating signals, and then at the receiver, the chaotic modulating signal is regenerated and divided from the receiver signal. Varying a smapling time interval to calibrate the robustness of the Lorenz discrete synchronized chaotic system as a nonlinear state estimator, we measured the performance of the Lorenz discrete syncrhonized chaotic system by comparing the synchronization error and the error between transmitted signal and received signal.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.22 no.12
• /
• pp.1698-1704
• /
• 2018

This paper presents a implementation of a chaotic Lorenz system for data secure communication applications. Here we have used PIC18F family-based microcontroller to generate the chaotic signal, and simulated waveform patterns confirm that the chaotic behavior of the microcontroller based discrete time chaotic Lorenz system. There are three R-2R ladder type A/D converters have been implemented for conversion of direct microcontroller digital output into analog waveform, utilizing this specific microcontroller relevant to this experiment work, microcontroller ports B, C and D have been utilized for its time waveform outputs X, Y and Z respectively. XC8 compiler used for the compilation of the program. MATLAB and PROTEUS software platforms are used for simulation. Finally, chaotic time wave forms, 2D chaotic attractors were obtained and secure communication analog waveforms were also verified by experimental measurement.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2018.10a
• /
• pp.487-489
• /
• 2018

This paper presents chaotic Lorenz system implementation for secure data communication applications. In this work chaotic signal is generated by a PIC18F family based microcontroller, XC8 compilers have been utilized for the compilation of C code of microcontroller program. For simulation work Matlab and Proteus platforms were utilized and finally, chaotic time waveforms, 2D and 3D chaotic attractor were obtained and secure communication waveforms were achieved successfully.

• Journal of Korea Water Resources Association
• /
• v.42 no.4
• /
• pp.355-363
• /
• 2009

The purpose of this paper is to investigate the influence of noise on chaotic time series. We used two time series of Lorenz system and of Great Salt Lake's volume data which are well known as chaotic systems. This study investigated the attractors, correlation dimensions, and Close Returns Plots and Close Returns Histograms of two time series to investigate the influence of noise as increasing noise level. We performed Chi-square test to the relative frequency of Close Returns Histogram from Close Returns Plot for the investigation of stochastic process of chaotic time series as increasing noise level of time series. As the results, two time series were changed from chaotic to stochastic series as noise level is increased. Finally, we analyzed the effect of noise cancellation by using Simple Moving Average method. The results of applications of Simple Moving Average method to Lorenz and GSL time series showed that we could effectively cancel the noise. Then we could confirm the applicability of Simple Moving Average method to cancel the noise for the hydrologic time series having chaotic characteristics.