Zengrong Liu

Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control.

This paper concerns the problem of exponential synchronization for a class of general delayed dynamical networks with hybrid coupling via pinning periodically intermittent control. Both the internal delay and coupling delay are taken into account in the network model. Meanwhile, the transmission delay and self-feedback delay are involved in the delayed coupling term. By establishing a new differential inequality, several simple and useful exponential synchronization criteria are derived analytically. It is shown that the controlled synchronization state can vary in comparison with the conventional synchronized solution, and the degree of the node and the inner delayed coupling matrix play important roles in the controlled synchronization state. By choosing different inner delayed coupling matrices and the degrees of the node, different controlled synchronization states can be obtained. Furthermore, the detail pinning schemes deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength are provided. The simple procedures illuminating how to design suitable intermittent controllers in real application are also given. Numerical simulations, including an undirected scale-free network and a directed small-world network, are finally presented to demonstrate the effectiveness of the theoretical results.

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.

Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

Homoclinic orbit in ODE on GAIM of the sine-Gordon equation

Abstract In this paper, the existence of the homoclinic orbit is proved under certain parametric conditions, by studying qualitative properties of ODE on GAIM of the sine-Gordon equation.

A simplified dynamic model for the p53-Mdm2 feedback loop

In this paper, a simplified dynamic model for the p53-Mdm2 feedback loop without the time lag effect of transcription is proposed. In the dynamic model, a nonlinear term is introduced to represent the dephosphorylation of the p53 protein. The results show that while the p53 and Mdm2 exhibit single pulse transient responses for the lower environmental stress stimulation, the sustained oscillations are observed for larger environmental stress stimulation. It is concluded that the simplified dynamic model is also able to reproduce the p53 and Mdm2 dynamic behaviors as shown in the experimental results and as predicted by previous complicated models in the literature. And the transcription time delay is dispensable for the p53 sustained oscillations. The results are helpful for understanding p53 dynamics.