Search

In this paper, we firstly develop fractional-degree Hénon maps with increasing and decreasing argument  n. Yin and Yang are two fundamental opposites in Chinese philosophy. Yin represents the moon and is the decreasing, negative, historical, or feminine principle in nature, while Yang represents the sun and is the increasing, positive, contemporary, or masculine principle in nature. Chaos produced by increasing n is called Yang chaos, that by decreasing nYin chaos, respectively. The simulation results show that chaos appears via positive Lyapunov exponents, bifurcation diagrams, and phase portraits. In order to examine the existence of chaotic behaviors in fractional-degree Yin–Yang Hénon maps, Feigenbaum’s constants are measured in this paper. It is found that the Feigenbaum’s constants in fractional-degree Yin–Yang Hénon maps are of great precision to the first and second Feigenbaum’s constants. A detailed analysis of the chaotic behaviors is also performed for the fractional-degree Hénon maps with increasing ( Yang) and decreasing ( Yin) argument  n. [ABSTRACT FROM AUTHOR]

Based on the Chinese philosophy, Yin is the decreasing, negative, historical or feminine principle in nature, while Yang is the increasing, positive, contemporary or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. Since the discrete Hénon map system is an invertible map, Yin–Yang T-S fuzzy model of chaotic Hénon map systems with increasing and decreasing argument can be studied. The Yang T-S fuzzy model of chaotic Hénon map system is presented. The Yin T-S fuzzy model of chaotic Hénon map system and Yin T-S fuzzy rules are obtained by invertible matrix in linear system theory. Chaos synchronization of Yang T-S fuzzy model of Hénon map systems is achieved by parallel distributed compensation technique, and the fuzzy controller for chaos synchronization of Yin T-S fuzzy model of Hénon map systems is also obtained by invertible matrix in linear system theory. The design of the Yin fuzzy controller is fleetly obtained by the inverse of Yang fuzzy controller, the concern is the Yin chaotic system must be an inverse of the Yang chaotic system. T-S fuzzy model scheme is used in the nonlinear discrete chaotic map system, so the nonlinear discrete chaotic map system can be analyzed by linear system theory. [ABSTRACT FROM PUBLISHER]

In recent years, there has been expanding research on the applications of fractional calculus to the areas of signal processing, modeling and controls. Analog circuit implementation of chaotic systems is used in studying nonlinear dynamical phenomena, which is also applied in realizing the controller development. In this paper, chain fractance and tree fractance circuits are constructed to realize the fractional-order Chen-Lee system. The results are in good agreement with those obtained from numerical simulation. This study shows that not only is this system related to gyro motion but can also be applied to electronic circuits for secure communication. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization of Yin and Yang chaotic T-S fuzzy Henon maps via PDC controllers. Based on the Chinese philosophy, Yin is the decreasing, negative, historical, or feminine principle in nature, while Yang is the increasing, positive, contemporary, or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. The Henon map is an invertible map; so the Henon maps with increasing and decreasing argument can be called the Yang and Yin Henon maps, respectively. Chaos synchronization of Yin and Yang T-S fuzzy Henon maps is achieved by PDC controllers. The design of PDC controllers is based on the linear invertible matrix theory. The T-S fuzzy model of Yin and Yang Henon maps and the design of PDC controllers are novel, and the simulation results show that the approach is effective. [ABSTRACT FROM AUTHOR]

The impulsive synchronization of two chaotic Chen-Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen-Lee systems was also implemented using an electronic circuit. [ABSTRACT FROM AUTHOR]

Synchronization of multiple identical chaotic systems, coupled in a ring structure, was studied in this paper. Ueda attractor was used as an example to perform the synchronization of several chaotic systems. The bound of the Ueda attractor was also estimated by numerical simulation. The above results were also adopted to design a controller to synchronize chaotic systems. The stability of the synchronization of multiple identical chaotic systems was investigated using Lyapunov's direct method. Some sufficient conditions of asymptotical synchronization were attained from rigorous mathematical theory. Further, numerical results were also demonstrated in order to validate the proposed synchronization approach. [ABSTRACT FROM AUTHOR]

Abstract: A new type for chaotically synchronizing systems, transient ladder chaos synchronization, is proposed in this Letter. For some physical systems, chaotic synchronization is possible in only some of the variables. It is shown that, for the non-synchronizing variable, synchronization up to a constant difference for is possible. The transient ladder chaos synchronization and anti-synchronization are illustrated by using two identical chaotic Froude pendulums. Numerical simulations are shown for demonstration. [Copyright &y& Elsevier]

Abstract: This paper presents a new hyper-chaotic system obtained by adding a nonlinear controller to the third equation of the three-dimensional autonomous Chen–Lee chaotic system. Computer simulations demonstrated the hyper-chaotic dynamic behaviors of the system. Numerical results revealed that the new hyper-chaotic system possesses two positive exponents. It was also found that the structure of the hyper-chaotic attractors is more complex than those of the Chen–Lee chaotic system. Furthermore, the hybrid projective synchronization (HPS) of the new hyper-chaotic systems was studied using a nonlinear feedback control. The nonlinear controller was designed according to Lyapunov’s direct method to guarantee HPS, which includes synchronization, anti-synchronization, and projective synchronization. Numerical examples are presented in order to illustrate HPS. [Copyright &y& Elsevier]