Since the beginning of the 90s a new direction appeared in the theory of dynamical systems, which was called “Controlling chaos”. The subject of this field is how to transform chaotic behavior to a regular one or to a more simple chaotic one by means of special small influence on the dynamical system. Pioneer works of this new direction were papers by Hubler and Lucher [1989], Jackson [1990] an...

This paper illustrates the presence of chaos in rank-one chaotic systems with delay via a binary test called 0-1 test for chaos. Chaotic synchronization between two rank-one chaotic systems without and with delay is achieved by means of Lyapunov functional and linear delayed feedback control method. Numerical simulations are implemented to verify the effectiveness of the proposed chaos synchron...

In the paper we propose a new synchronization principle. To guarantee synchronization between coupled chaotic oscillators, proper coupling constants are selected by the Liapunov stability theory and Hurwitz Theorem. As an example and application, we prove the conjecture [Wu & Chua, 1994] that synchronization between two chaotic Chua’s circuits can be achieved by using the second state as feedba...

The problem of the dual synchronization of two different fractional-order chaotic systems is studied. By a linear controller, we realize the dual synchronization of fractional-order chaotic systems. Finally, the proposed method is applied for dual synchronization of Van der Pol-Willis systems and Van der Pol-Duffing systems. The numerical simulation shows the accuracy of the theory.

Adaptive control technique is used to design suitable controllers to synchronize two different coupled chaotic systems with uncertainties. The information signal hidden in chaotic signal is transmitted and then successfully recovered at the receiver once synchronization is achieved. Different chaotic systems with uncertainties are chosen respectively as the transmitter and receiver systems to e...

This paper designs four simple adaptive feedback controllers for chaos synchronization with linear– nonlinear decomposition method. Synchronization of two identical chaotic systems is realized by designed controller; Synchronization of two different chaotic systems is also realized, and the proposed method is simple and robust. Numerical simulations are given to show the effectiveness of this m...

In this paper, the generalized Hamiltonian system approach was applied to the synchronization of chaotic systems. The synchronization is between the transmitter and the receiver dynamics. The synchronization of several chaotic systems is studied by the method, respectively. The numerical results are in very good agreement with the theoretical analysis.

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adapti...

A function projective synchronization is defined to synchronize two different systems up to a scaling function matrix f with different initial values. The function projective synchronization is more general than the complete synchronization, the generalized projective synchronization and the modified projective synchronization. The corresponding framework of synchronization is set up and used t...

Encoded information based on synchronization of coupled chaotic Nd:YAG lasers in master-slave configuration is numerically studied. Encoding, transmission, and decoding of information in optical chaotic communication with a single channel is presented. We analyze the robustness of the encrypted audio transmission in a channel noise. In order to illustrate this synchronization robustness, we pre...