Shuiming Cai

Exponential synchronization of chaotic systems with time-varying delays and parameter mismatches via intermittent control.

This paper studies the synchronization of coupled chaotic systems with time-varying delays in the presence of parameter mismatches by means of periodically intermittent control. Some novel and useful quasisynchronization criteria are obtained by using the methods which are different from the techniques employed in the existing works, and the derived results are less conservative. Especially, a strong constraint on the control width that the control width should be larger than the time delay imposed by the current references is released in this paper. Moreover, our results show that the synchronization criteria depend on the ratio of control width to control period, but not the control width or the control period. Finally, some numerical simulations are given to show the effectiveness of the theoretical results.

The interaction between multiplex community networks

Multiplex community networks, consisting of several different types of simplex networks and interconnected among them, are ubiquitous in the real world. In this paper, we carry out a quantitative discussion on the interaction among these diverse simplex networks. First, we define two measures, mutual-path-strength and proximity-node-density, based on twoplex community networks and then propose an impact-strength-index (ISI) to describe the influence of a simplex network on the other one. Finally, we apply the measure ISI to make an explanation for the challenge system of social relations from the viewpoint of network theory. Numerical simulations show that the measure ISI can describe the interaction between multiplex community networks perfectly.

Emergence of modularity and disassortativity in protein-protein interaction networks

In this paper, we present a simple evolution model of protein-protein interaction networks by introducing a rule of small-preference duplication of a node, meaning that the probability of a node chosen to duplicate is inversely proportional to its degree, and subsequent divergence plus nonuniform heterodimerization based on some plausible mechanisms in biology. We show that our model cannot only reproduce scale-free connectivity and small-world pattern, but also exhibit hierarchical modularity and disassortativity. After comparing the features of our model with those of real protein-protein interaction networks, we believe that our model can provide relevant insights into the mechanism underlying the evolution of protein-protein interaction networks.

Robust impulsive synchronization of uncertain delayed dynamical networks

The present paper deals with the issues of robust impulsive synchronization of uncertain complex delayed dynamical networks from the view of dynamics and control. The prime characteristic of the model considered here is that the coupling functions can be linear or nonlinear, even unknown, which can well describe practical architectures of more realistic networks. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criteria are derived for synchronization of such dynamical network. Furthermore, the theoretical results are applied to a typical specific network composing of the representative chaotic delayed Hopfield neural network nodes, and numerical simulations are given to verify the theoretical results.