Narrow Results

This paper considers the synchronization and anti-synchronization problem of N different coupled chaotic systems with ring connections. Employing the direct design method to design the synchronization and anti-synchronization controllers which can transform the error systems into a stable system with special anti-symmetric structure. Some simple stability criteria are then derived for reaching the synchronization in such systems. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical.

Asynchronous temporal Boolean Networks (ATBNs) are more complex in structure and have different linear expressions compared to traditional synchronous Boolean networks. The complexity depends on the number of updated nodes. The main contribution of this paper is to propose results of synchronization and anti-synchronization problems of ATBNs. First, this paper abstracts two Temporal Boolean Networks (TBNs) into a mathematical model, and provides a linear expression of the network by means of the semi-tensor product (STP) tool. Second, based on the asynchronous updating scheme of temporal Boolean networks, we investigate the synchronization (including complete synchronization and anti-synchronization) of ATBNs, and provide two results to guarantee the synchronization and anti-synchronization. Finally, we provide two examples to verify the correctness of our theorems and corollaries.

This paper analyzes anti-synchronization of three-dimensional autonomous chaotic systems and achieves the anti-synchronization of a class of three-dimensional autonomous chaotic systems, i.e., Lorenz system, Chen system, and Lü system with one another via active control. Numerical simulations are demonstrated to verify the effectiveness of the proposed method.

Anti-synchronization between different hyperchaotic systems is presented using the Chen and a new system. When the parameters of two systems are known, one can apply active synchronization method. When the parameters are unknown or uncertain, one can apply adaptive synchronization method. The simulation results verify the effectiveness of the proposed two schemes.

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.

This paper analyzes a coupled dynamic system. Based on the stability criterion of linear systems, a new approach for constructing chaotic synchronization and anti-synchronization is proposed. The complete synchronizations and anti-synchronizations of the coupled dynamic system are achieved via the linear separation method. Finally, the method is applied in security communication. Numerical simulations are provided for illustration and verification of the proposed method.

Proportional delay is a class of unbounded time-varying delay. A class of bidirectional associative memory (BAM) memristive neural networks with multiple proportional delays is concerned in this paper. First, we propose the model of BAM memristive neural networks with multiple proportional delays and stochastic perturbations. Furthermore, by choosing suitable nonlinear variable transformations, the BAM memristive neural networks with multiple proportional delays can be transformed into the BAM memristive neural networks with constant delays. Based on the drive-response system concept, differential inclusions theory and Lyapunov stability theory, some anti-synchronization criteria are obtained. Finally, the effectiveness of proposed criteria are demonstrated through numerical examples.

In this paper, the issue of synchronization and anti-synchronization for fractional-delayed memristor-based chaotic system is studied by using active control strategy. Firstly, some explicit conditions are proposed to guarantee the synchronization and anti-synchronization of the proposed system. Secondly, the influence of order and time delay on the synchronization (anti-synchronization) is discussed. It reveals that synchronization (anti-synchronization) is faster as the order increases or the time delay decreases. Finally, some numerical simulations are presented to verify the validity of our theoretical analysis.

This paper is concerned with the asymptotic anti-synchronization problem of the memristor-based bidirectional associative memory neural networks (MBAMNNs) and its application in network secure communication. First, we propose a new model of MBAMNNs with probabilistic delays. By establishing a Bernoulli distributed stochastic variable, the information of transmittal time-varying delays is studied. Second, in order to provide a more robust and secure system, we develop a new anti-synchronization model based on the MBAMNNs. The adaptive laws are carefully designed to confirm the process of encryption and decryption in networks secure communication system. Finally, several numerical examples are presented to demonstrate the effectiveness and applicability of our proposed mechanism.

As a special case of generalized synchronization, chaos anti-synchronization can be characterized by the vanishing of the sum of relevant variables. In this paper, based on Lyapunov stability theorem for ordinary differential equations, several sufficient conditions for guaranteeing the existence of anti-synchronization in a class of coupled identical chaotic systems via linear feedback or adaptive linear feedback methods are derived. Chua's circuit is presented as an example to demonstrate the effectiveness of the proposed approach by computer simulations.

This paper demonstrates that complete synchronization and antisynchronization can coexist in 4D systems by direct linear coupling. Theoretical analysis and numerical simulation show that two different types of synchronization can simultaneously be achieved.