Hsien-Keng Chen

The Stability of Chaos Synchronization of the Japanese Attractors and its Application

The synchronization of chaos of the two identical chaotic motions of the Japanese attractor has been studied. First, the stability of the chaos synchronization of the systems is investigated by Liapunovs direct method. Some sufficient conditions of global asymptotic synchronization are attained from rigorous mathematical theory. It has also been demonstrated numerically that applying two different kinds of one-way coupling technology can synchronize the two identical chaotic systems. The sign of the sub-Liapunov exponent has been used as an indicator for the occurrence of chaos synchronization. Chaos synchronization can be assured as shown well by phase trajectory. In addition, the chaotic signals are used to mask the message function in the secure communication system.

Synchronization of chaotic symmetric gyros by one-way coupling conditions

Abstract A simple satellite is a symmetric gyro. Satellites are used for communications, weather forecasts, surveying and in several other scientific and military applications. In particular, for military use secure communications are very important. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyros. It has been demonstrated that applying four different kinds of one-way coupling conditions can synchronize two identical chaotic systems. The sign of the sub-Liapunov exponent has been used as an indicator for the occurrence of chaos synchronization. It has also been found that when chaos synchronization occurs the positive major sub-Liapunov exponent transverses the zero value and becomes negative for the last time. Chaos synchronization can also be shown by phase trajectory. In addition, synchronization time is also examined. Furthermore, it has been found that different distances of the initial conditions between the master system and slave system do not affect the occurrence of chaos synchronization.

Parametric Analysis and Impulsive Synchronization of Fractional-Order Newton-Leipnik Systems

In this paper, the influences of parameters on the dynamics of a fractional-order Newton-Leipnik system were numerically studied. Impulsive synchronization of two fractional-order Newton-Leipnik systems was also investigated. The ranges of the parameters used in this study were relatively broad. The system displayed comprehensive dynamic behaviours, such as fixed points, periodic motion (including periodic-3 motion), chaotic motion, and transient chaos. A period-doubling route to chaos in this study was also found. Sufficient conditions on synchronization of the two systems are provided and illustrative example is given.

IMPLEMENTATION OF THE FRACTIONAL-ORDER CHEN-LEE SYSTEM BY ELECTRONIC CIRCUIT

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 syst...

Pragmatical adaptive synchronization – New fuzzy model of two different and complex chaotic systems by new adaptive control

Abstract In this paper, (1) a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and (2) a new adaptive approach and a new control Lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors. By using this new model, the numbers of fuzzy rules of chaotic systems can be reduced from 2 N to 2 × N and only 2 subsystems are needed, where N is the number of nonlinear terms. The fuzzy systems become much simpler. In addition, through the new fuzzy model, the new fuzzy systems are much simpler than T–S fuzzy systems (when nonlinear systems are complicated) and can be used to any other kind of application in fuzzy logic control or fuzzy modeling. Mathieu–Van der Pol system (which is called M–V system in this paper) and Quantum cellular neural networks nanosystem (which is called Q-CNN system in this paper) are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control Lyapunov function. The T–S fuzzy modeling and traditional adaptive control are also given in Appendix B T–S fuzzy model of chaotic systems , Appendix C Traditional adaptive method for comparison.

Application of advanced process control in plastic injection molding

This research applies Advanced Process Control (APC)-based injection molding system to improve the quality of products. The relationships between the input parameters (injection velocity, injection pressure, injection time and barrel temperature) and a single output variable (the weight of product) were found through an experimental design method. Moreover, the injection molding process model was built via a multiple regression analysis. A dynamic model turning minimum variance (DMTMV) method is utilized to control the process. Quantified improvements were further obtained from experiments.

Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems

A hybrid stability checking method is proposed to verify the establishment of synchronization between two hyperchaotic systems. During the design stage of a synchronization scheme for chaotic fractional-order systems, a problem is sometimes encountered. In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. We propose a new and efficient hybrid method to verify the stability in this situation. The passivity-based control scheme for synchronization of two hyperchaotic fractional-order Chen-Lee systems is provided as an example. Theoretical analysis of the proposed method is validated by numerical simulation in time domain and examined in frequency domain via electronic circuits.

Complete synchronization of two Chen-Lee systems

This study demonstrates that complete synchronization of two Chen-Lee chaotic systems can be easily achieved. The upper bound of the Chen-Lee chaotic system is estimated numerically. A controller is designed to synchronize two chaotic systems. Sufficient conditions for synchronization are obtained using Lyapunovs direct method. Two numerical examples are presented to verify the proposed synchronization approach.

Design of PDC Controllers by Matrix Reversibility for Synchronization of Yin and Yang Chaotic Takagi-Sugeno Fuzzy Henon Maps

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.

IMPULSIVE SYNCHRONIZATION AND ITS IMPLEMENTATION IN CHEN–LEE SYSTEMS

The impulsive synchronization of two chaotic Chen–Lee systems was investigated in this paper. Based on Lyapunovs 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.