The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding–decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding–decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.

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Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding–Decoding-Based Approach

In this paper, we introduce two complex dynamical networks with multiweights, which have several different sorts of weights between two nodes. By means of Lyapunov functional method and pinning control technique, some sufficient conditions are derived to ensure the synchronization for proposed network models. Moreover, some adaptive strategies are given to acquire suitable coupling strengths and feedback gains. By exploiting these designed adaptive laws, several general criteria for network synchronization are established. Finally, two numerical examples are also provided to show the validity of the theoretical results.

Pinning Synchronization of Complex Dynamical Networks With Multiweights

The output synchronization and H∞ output synchronization problems for multiweighted complex network are discussed in this paper. First, we analyze the output synchronization of multiweighted complex network by exploiting Lyapunov functional and Barbalat's lemma. In addition, some nodes- and edges-based pinning control strategies are developed to ensure the output synchronization of multiweighted complex network. Similarly, the H∞ output synchronization problem of multiweighted complex network is also discussed. Finally, two numerical examples are presented to verify the correctness of the obtained results.

Analysis and Pinning Control for Output Synchronization and H∞ Output Synchronization of Multiweighted Complex Networks.

Finite-time synchronization of multi-weighted complex dynamical networks with and without coupling delay

A multi-weighted network model with different dimensions of output and input vectors is studied in this paper. First, we analyze the passivity of the proposed network model by employing some inequality techniques and Lyapunov functional method, and give a synchronization condition for output-strictly passive complex dynamical network with multi-weights (CDNMWs). Furthermore,  by using pinning adaptive strategies to control a small portion of nodes or edges, some sufficient conditions for ensuring passivity of CD-NMWs are presented. In addition, when CDNMWs under the designed pinning adaptive control strategies are  output-strictly  passive, two synchronization criteria are also established. Finally, two examples are given to show the validity of the obtained results.

Passivity Analysis and Pinning Control of Multi-Weighted Complex Dynamical Networks

On the basis of traditional weighted network, we study a new complex network model with multi-weights, which has one or several different types of weights between any two nodes. According to the method of network split, we split the complex network with multi-weights into several different complex networks with single weight, and study its global synchronization. Taking bus lines as the network nodes, a new public traffic roads network model with multi-weights is established by the proposed network model and space R modeling approach. Then based on the Lyapunov stability theory, the criteria is designed for the global synchronization of the public traffic roads networks with multi-weights. By changing the different weights and taking the Lorenz chaotic system for example, some numerical examples are given to discuss the balance of the whole public traffic roads network.

Synchronization analysis of complex networks with multi-weights and its application in public traffic network

Regarding single bus transfer junction as a research object, this paper constructs the urban traffic network models with multi-weights taking different bus lines in bus transfer junction as the network nodes, that is, the urban traffic network with multi-weights is given different properties weights at every edge. According to the method of network split, the complex network with multi-weights is split into several different single weighted complex networks. Then, we study the global synchronization of the new network model by changing congestion degrees, transfers coefficient and passenger flow density between different bus lines. Finally, analytical and simulated results are given to show the impact of different properties weights to the public traffic network balance.

Research on urban public traffic network with multi-weights based on single bus transfer junction

Compared with integer order chaotic systems, fractional order chaotic systems can reflect natural phenomena more accurately, which are more suitable for chaotic cryptosystems. In order to explore the application of fractional order chaotic system in cryptography, a novel fractional order hyperchaotic system is constructed and implemented on DSP platform. More progressively, based on Adomian decomposition method, the dynamic behavior is studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum and spectral entropy (SE) complexity. It is found that each parameter and order have a large range of intervals that can keep the system in a hyperchaotic state. Therefore, the hyperchaotic sequences generated by the constructed fractional order hyperchaotic system have sufficient randomness and are well suited for applications in secure communications. In addition, a color image encryption scheme is designed based on the fractional order hyperchaotic system and DNA dynamic coding. Firstly, the improved Arnold algorithm is used to scramble the original image, then the column cyclic shift method is applied for secondary scrambling, and finally the pixel value is diffused by DNA sequence operation. The security analysis results indicate that the designed encryption algorithm can not only encrypt images effectively, but also has high security and can resist various common attacks.

Dynamic analysis of a fractional-order hyperchaotic system and its application in image encryption

In this paper, we discussed the fixed points and their linear stability of a new nonlinear autonomous system that introduced by J.C. Sprott. Based on Lyapunov stabilization theorem, a global chaos synchronization scheme of three coupled identical systems is investigated. By choosing proper coupling parameters, the states of all the three systems can be synchronized. Then this method was applied to secure communication through chaotic masking, used three coupled identical systems, propose a novel method of chaos encryption, after encrypting in the previous two transmitters, information signal can be recovered exactly at the receiver end. Simulation results show that the method can realize monotonous synchronization. Further more, the information signal can be recovered undistorted when applying this method to secure communication.

Li Zhang

Papers

Synchronization analysis of complex networks with multi-weights and its application in public traffic network

Research on urban public traffic network with multi-weights based on single bus transfer junction

Dynamic analysis of a fractional-order hyperchaotic system and its application in image encryption

Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption

Dynamics explore of an improved HR neuron model under electromagnetic radiation and its applications