Liu Zhongxin

Dynamic spreading behavior of homogeneous and heterogeneous networks

Abstract The detailed investigation of the dynsmic epidemic spreading on homogeneous and heteiogeneous networks was carried out. After the analysis of the basic epidemic models, the susceptible-infected-susceptible (SIS) model on homogenous and heterogeneous networks is established, and the dynamical evolution of the density of the infected individuals in these two different kinds of networks is analyzed theoretically. It indicates that heterogeneous networks sre easier to piopagate for the epidemics and the leading spreading behavior is dictated by the exponential increasing in the initial outbreaks. Large-scale simulations display that the infection is much faster on heterogeneous networks than that on homogeneous ones. It means that the network topology can have a significant effect on the epidemics taking place on complex networks. Some containment sfrategies of epidemic outbreaks sre presented according to the theoretical analyses and numerical simulations. * Supported by National Natural Science Fou...

Relations between structural properties and synchronizability on local world dynamical networks

Abstract In this paper, the effects of various structural properties on the synchronization of coupled oscillators with local-world coupling configurations are investigated. It is found that for local world networks, the larger heterogeneity of the degree distribution, the enhanced interconnection of nodes, and the increased clustering do not improve the synchronizability of dynamical systems. On the contrary, the increase of maximum betweenness centrality appears to be responsible for the decrease of the synchronizability. * Supported by National Natural Science Foundation of China (Grant No. 60574036), the Program for New Century Excellent Talents in University of China (NCET), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20050055013)

Movement Control of Multi-Agent System with Multiple Leader Based on Potential Function

A new control method based on potential function is presented, which can effectively control the movement of multi-agent system with multiple leaders. The system includes two kinds of agent: leader and follower. Leader has the knowledge about the environment and is attracted by the object, but follower is only affected by the information about the neighbor. To make the system to the anticipation, proper potential functions related to the environment and the object is chosen, and different control law is designed for the two kinds of agents, and stability analysis and simulation are made in the end.

Semi-tensor product of matrices approach to stability and stabilization analysis of bounded Petri net systems

In this paper, we investigate the problems of stability and stabilization for bounded Petri net systems (BPNSs) by using the semi-tensor product (STP) of matrices. First, a new matrix equation, under the framework of Boolean algebra, is established, and is based on our previous results presented on the marking evolution equation of BPNSs. This equation made it possible to provide the necessary and sufficient condition for the equilibrium point stability of BPNSs. Second, the problem associated with marking feedback stabilizability is solved by introducing the concept and some properties of the marking pre-reachability set of BPNSs, respectively. By resorting to these properties, the necessary and sufficient condition for equilibrium point stabilization is presented. In addition, a design procedure is proposed to find all the optimal marking feedback controllers that implement the minimal length trajectories from each marking to the equilibrium point. The proposed results, in this paper, are based on the matrix form, thus the problems of verifying the stability and stabilization of BPNSs are expressed in the matrix computation. This is very simple and straightforward work by means of the MATLAB toolbox of the STP of matrices. The proposed results are of a very simple form and can conveniently be implemented on a computer. Finally, several examples are presented to illustrate the validity and application of the proposed approaches.

A continuous second-order sliding mode guidance against highly maneuverable targets

Conventional proportional navigation or augmented proportional navigation guidance laws are widely used for intercepting maneuverable targets; however, they are effective only in intercepting a target with a constant velocity or a known acceleration. In this paper, a continuous second-order sliding mode guidance law is designed to intercept a highly maneuverable target in connection with the super-twisting algorithm. Meanwhile, the target maneuver information, regarded as unpredictable disturbance, is coped with by an extended state observer (ESO) and then is compensated in the guidance law. In the proposed guidance scheme, no information about target motion is needed. The closed-loop error can be guaranteed to be bounded by using Lyapunov method. The simulation results demonstrate the effectiveness and robustness of the proposed guidance method against a highly maneuverable target.