Hui Liu

Structure identification of uncertain general complex dynamical networks with time delay

It is well known that many real-world complex networks have various uncertain information, such as unknown or uncertain topological structure and node dynamics. The structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. At the same time, time delay often appears in the state variables or coupling coefficients of various practical complex networks. This paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay. In particular, this method is also effective for uncertain delayed complex dynamical networks with different node dynamics. Moreover, the proposed method can be easily extended to monitor the on-line evolution of network topological structure. Finally, three representative examples are then given to verify the effectiveness of the proposed approach.

Coupling Strength Allocation for Synchronization in Complex Networks Using Spectral Graph Theory

Using spectral graph theory and especially its graph comparison techniques, we propose new methodologies to allocate coupling strengths to guarantee global complete synchronization in complex networks. The key step is that all the eigenvalues of the Laplacian matrix associated with a given network can be estimated by utilizing flexibly topological features of the network. The proposed methodologies enable the construction of different coupling-strength combinations in response to different knowledge about subnetworks. Adaptive allocation strategies can be carried out as well using only local network topological information. Besides formal analysis, we use simulation examples to demonstrate how to apply the methodologies to typical complex networks.

An Encryption Scheme Based on Synchronization of Two-Layered Complex Dynamical Networks

A novel encryption scheme based on complex chaotic networks is proposed in this paper. Compared with a single chaotic system, a network of chaotic systems possesses complex dynamic characteristics, which can be used in encryption to enhance security. We adopt the drive-response synchronization method to synchronize two identical chaotic networks at the transmitter and receiver. Analysis on encryption security shows that key space is enlarged exponentially with respect to the number of nodes in the drive network, and also shows that the encryption system is highly sensitive to parameter mismatch. The proposed scheme is competent in carrying out encryption tasks of large data. Both theoretical and numerical results demonstrate that the proposed scheme is feasible for implementation in image and data encryption.

Synchronization in Directed Complex Networks Using Graph Comparison Tools

This paper proposes lower bounds for the coupling strengths of oscillators in directed networks to guarantee global synchronization. The novel idea of graph comparison from spectral graph theory is employed so that the combinatorial features of a given network can be fully utilized to simplify computations. For large networks that can be decomposed into a set of smaller strongly connected components, the comparison can be carried out at the local level as well. To validate theoretical analysis, examples are provided to demonstrate how to apply the proposed methodologies to typical directed complex networks.

New spectral graph theoretic conditions for synchronization in directed complex networks

This paper proposes lower bounds for the coupling strengths of oscillators in directed networks to guarantee global synchronization. The novel idea of graph comparison from spectral graph theory is employed so that the topological features of a given network can be fully utilized to simplify computations. For large networks that can be decomposed into a set of smaller strongly connected components, the comparison can be carried out at the local level as well.

Topology identification of an uncertain general complex dynamical network

In real-world complex networks, there exists many uncertain information, such as uncertain topological structures and uncertain system parameters. Without question, the topology identification and parameter identification are two traditionally challenging questions in complex networks. Based on the adaptive observers, our approach can identify the topological structures and system parameters of the uncertain complex dynamical networks together. In particular, our method is also very effective for the complex networks with different node dynamics. Moreover, the proposed approach can be used to monitor the online evolution of network topological structures and system parameters. Finally, several typical simulations are used to verify the effectiveness of the proposed approach.

Coordinate-free formation control of multi-agent systems using rooted graphs

Abstract This paper studies how to control large formations of autonomous agents in the plane, assuming that each agent is able to sense relative positions of its neighboring agents with respect to its own local coordinate system. We tackle the problem by adopting two types of controllers. First, we use the classical gradient-based controllers on three leader agents to meet their distance constraints. Second, we develop other type of controllers for follower agents: utilizing the properties of rooted graphs, one is able to design linear controllers incorporating relative positions between the follower agents and their neighbors, to stabilize the overall large formations. The advantages of the proposed method are fourfold: (i) fewer constraints on neighboring relationship graphs; (ii) simplicity of linear controllers for follower agents; (iii) global convergence of the overall formations; (iv) implementation in local coordinate systems, in no need of a global coordinate system. Numerical simulations show the effectiveness of the proposed method.

A Weighted Multi-Local-World Network Evolving Model and Its Application in Software Network Modeling

The phenomenon of local worlds (also known as communities) exists in numerous real-life networks, for example, computer networks and social networks. We proposed the Weighted Multi-Local-World (WMLW) network evolving model, taking into account the dense links between nodes in a local world, the sparse links between nodes from different local worlds, and the different importance between intra-local-world links and inter-local-world links. On topology evolving, new links between existing local worlds and new local worlds are added to the network, while new nodes and links are added to existing local worlds. On weighting mechanism, weight of links in a local world and weight of links between different local worlds are endowed different meanings. It is theoretically proven that the strength distribution of the generated network by the WMLW model yields to a power-law distribution. Simulations show the correctness of the theoretical results. Meanwhile, the degree distribution also follows a power-law distribution. Analysis and simulation results show that the proposed WMLW model can be used to model the evolution of class diagrams of software systems.

CFD Prediction of Airfoil Drag in Viscous Flow Using the Entropy Generation Method

A new aerodynamic force of drag prediction approach was developed to compute the airfoil drag via entropy generation rate in the flow field. According to the momentum balance, entropy generation and its relationship to drag were derived for viscous flow. Model equations for the calculation of the local entropy generation in turbulent flows were presented by extending the RANS procedure to the entropy balance equation. The accuracy of algorithm and programs was assessed by simulating the pressure coefficient distribution and dragging coefficient of different airfoils under different Reynolds number at different attack angle. Numerical data shows that the total entropy generation rate in the flow field and the drag coefficient of the airfoil can be related by linear equation, which indicates that the total drag could be resolved into entropy generation based on its physical mechanism of energy loss.

Synchronization regions of discrete-time dynamical networks with impulsive couplings

Abstract This paper deals with synchronization of a class of discrete-time dynamical networks. First, a novel model for discrete-time dynamical networks with impulsive couplings between nodes is proposed. Second, both global and local stability of synchronization manifold is investigated using the multiple Lyapunov function method and some inequality techniques. As a result, several synchronization criteria are obtained. Third, two illustrative examples are given to validate the effectiveness of the proposed synchronization criteria. Analysis on the synchronization regions of the discrete-time dynamical network with metapopulation dynamics is further made, which reveals such a finding that either a relatively large coupling strength or a short impulsive interval is not necessarily beneficial to synchronization of the discrete-time dynamical network.