• Journal of Korea Society of Industrial Information Systems
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• v.6 no.4
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• pp.75-80
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• 2001

In this paper, we propose a new chaotic synchronization algorithm of using HVPM(Hyperchaotic Volume Preserving Maps) model. The proposed chaotic equation, that is, HVPM model which consists of three dimensional discrete-time simultaneous difference equations and shows uniquely random chaotic attractor using nonlinear maps and modulus function. Pecora and Carrol have recently shown that it is possible to synchronize a chaotic system by sending a signal from the drive chaotic system to the response subsystem. We proposed coupled synchronization algorithm in order to accomplish discrete time hyperchaotic HVPM signals. In the numerical results, two hyperchaotic signals are coupled and driven for accomplishing to the chaotic synchronization systems. And it is demonstrated that HVPM signals have shown the chaotic behavior and chaotic coupled synchronization.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.2
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• pp.91-97
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• 2014

Chaotic dynamics is an active research area in fields such as biology, physics, sociology, psychology, physiology, and engineering. Interest in chaos is also expanding to the social sciences, such as politics, economics, and societal events prediction. Most people pursue happiness, both spiritual and physical in many cases. However, happiness is not easy to define, because people differ in how they perceive it. Happiness can exist in mind and body. Therefore, we need to be happy in both simultaneously to achieve optimal happiness. To do this, we need to synchronize mind and body. In this paper, we propose a chaotic synchronization method in a mathematical model of happiness organized by a second-order ordinary differential equation with external force. This proposed mathematical happiness equation is similar to Duffing's equation, because it is derived from that equation. We introduce synchronization method from our mathematical happiness model by using the derived Duffing equation. To achieve chaotic synchronization between the human mind and body, we apply an idea of mind/body unity originating in Oriental philosophy. Of many chaotic synchronization methods, we use only coupled synchronization, because this method is closest to representing mind/body unity. Typically, coupled synchronization can be applied only to non-autonomous systems, such as a modified Duffing system. We represent the result of synchronization using a differential time series mind/body model.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2005.05a
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• pp.215-221
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• 2005

In this paper, we propose a method to a synchronization of chaotic UAVs that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. The proposed methods are assumed that if one of two chaotic UAVs receives the synchronization command, the other UAV also follows the same trajectory during chaotic UAVs search on the arbitrary surface.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.293-320
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• 2014

In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstepping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability theory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predetermined desired value. The adaptive backstepping control method is effective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the flexibility to construct a control law and estimate the parameter values. Numerical simulations are also given to illustrate and validate the synchronization results derived in this paper.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.7
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• pp.1616-1623
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• 2005

In this paper, we propose that the synchronization method for mutual cooperative control in the chaotic mobile robot. In order to achieve the synchronization for mutual cooperative control in the chaotic mobile robot, we apply coupled synchronization technique and driven synchronization technique in the chaotic mobile robot without obstacle and with obstacle.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2852-2854
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• 2005

In this paper, we propose a method to a synchronization of chaotic mobile robots that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a VDP (Van der Pol) equation with an unstable limit cycle. The proposed methods are assumed that if one of two chaotic mobile robot receives the synchronization command, the other robot also follows the same trajectory during the chaotic robot search on the arbitrary surface.

• 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.

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

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.4
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• pp.617-621
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• 2012

This paper considers the synchronization problem of chaotic systems. For this problem, the sampled-data control approach is used to achieve asymptotic synchronization of two identical chaotic systems. Based on Lyapunov stability theory, a new stability condition is obtained via linear matrix inequality formulation to find the sampled-data feedback controller which achieves the synchronization between chaotic systems. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.563-586
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• 2015

In this research work, a seven-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed. The basic qualitative properties of the novel jerk chaotic system have been described in detail. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed for the 3-D novel jerk chaotic system.