• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.457-478
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• 2014

In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

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

• KEPCO Journal on Electric Power and Energy
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• v.2 no.4
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• pp.563-567
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• 2016

In this paper, the chaos-based secure scheme for power line communication is proposed for the first time. A digitalized chaotic generator based Lorenz system is utilized for generating nonlinear dynamic chaotic signal for masking the information signal instead of reported analog chaotic generators. A simple method of encryption and decryption is also given. In order to confirm the feasibility of the proposed scheme, the system is simulated using a simplified encryption/decryption method in Proteus. The gained results from simulation demonstrated that by using the chaos-based security method, the data can be encrypted and easily transmitted through the power line network efficiently.

• Industrial Engineering and Management Systems
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• v.14 no.3
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• pp.312-317
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• 2015

The dynamic system approach in time series has been used in many real problems. Based on Taken's embedding theorem, we can build the predictive function where input is the time delay coordinates vector which consists of the lagged values of the observed series and output is the future values of the observed series. Although the time delay coordinates vector from multivariate time series brings more information than the one from univariate time series, it can exhibit statistical redundancy which disturbs the performance of the prediction function. We apply dimension reduction techniques to solve this problem and analyze the effect of this approach for prediction. Our experiment uses delayed Lorenz series; least squares support vector regression approximates the predictive function. The result shows that linearly preserving projection improves the prediction performance.

• 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.

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

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.437-440
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• 1998

In this paper, the design method of fuzzy neural network(FNN) controller using indirect adaptive control technique is presented for controlling chaotic nonlinear systems. Firstly, the fuzzy model identified with a FNN in off-line process. Secondly, the trained fuzzy model tunes adaptively the control rules of the FNN controller in on-line process. In order to evaluate the proposed control method, Indirect adaptive control method is applied to the representative continuous-time chaotic nonlinear systems, that is, the Duffing system and the Lorenz system. Simulations are done to verify the effectivencess of controller.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.985-989
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• 2005

This paper presents chaos synchronization between two different chaotic systems using nonlinear control method. The proposed technique is applied to achieve chaos synchronization for the Lorenz and Rossler dynamical systems. Numerical simulations are also implemented to verify the results.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.516-521
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• 1998

본 논문에서는 비선형 시스템 해석 문제에 널리 이용되고 있는 퍼지 시스템(Fuzzy System)과 신경 회로망(MlPNN)의 성능을 평가하기 위해 비선형 예측기를 구성하였고 두 예측기를 비선형 시계열(Time Series) 예측 문제에 적용하여 두 예측기의 성능을 비교 분석하였다. 예측 실험을 위한 데이터로 Mackey-Glass와 Lorenz 시계열을 사용하였다.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.5
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• pp.747-754
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• 2017

Chaos-based secure communication systems are alternative of standard spread-spectrum systems that enable spreading the spectrum of the information signals and encrypting information signals with simple and inexpensive chaotic circuitry. In secure communication area, like Lorenz, Chua, Rossler, Duffing etc, classical systems are widely used. Malasoma chaotic system is topologically simple but their dynamical behaviors are non-linear synchronization and secure communication applications has not seen in paper. This paper aims for introducing a new chaotic system which is able to use as alternative to classical chaotic systems into secure communication fields. In addition, this new model simulates a synchronous communication system using P-C (Pecora-Carroll) method by verifying security with chaos signal through simulation. Modelling, synchronization and secure communication applications of Malasoma are realized respectively in MATLAB-Simulink environment. Retrieved results show that this novel chaotic system is able to use in secure communication fields.