Liu Zeng-rong

Generalized Synchronization of Discrete Systems

Generalized synchronization of two discrete systems was discussed. By constructing appropriately nonlinear coupling terms, some sufficient conditions for determining the generalized synchronization between the drive and response systems were derived. In a positive invariant and bounded set, many chaotic maps satisfy the sufficient conditions. The effectiveness of the sufficient conditions is illustrated by three examples.

Impulsive Control for the Stabilization of Discrete Chaotic System

We first give the theoretical result of the stabilization of general discrete chaotic systems by using impulsive control. As an example and an application of the theoretical result, we derive some sufficient conditions for the stabilization of the double rotor map via impulsive control. The computer simulation result is given to demonstrate the method.

Synchronization between Different Networks

Synchronization between two networks with different topology structures and different dynamical behaviours is studied. These two different networks are driving and responding networks, respectively. Under the preconditions that the driving network gets synchronization, we give the conditions for the responding network to be synchronized to the same dynamics as the driving network with the help of the open-plus-closed-loop method. Then a example is given to verify the validity of the theoretical results.

Impulsive Synchronization of Discrete Chaotic Systems

Impulsive synchronization of two chaotic maps is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two chaotic maps by using synchronization impulses with varying impulsive intervals. As an example and application of the theorem, we derives some sufficient conditions for the synchronization of two chaotic Lozi maps via impulsive control. The effectiveness of this approach has been demonstrated with chaotic Lozi map.

Wavelet basis analysis in perturbed periodic KdV equation

In the paper by using the spline wavelet basis to construct the approximate inertial manifold, we study the longtime behavior of perturbed perodic KdV equation.

Duplication: a Mechanism Producing Disassortative Mixing Networks in Biology

Assortative/disassortative mixing is an important topological property of a network. A network is called assortative mixing if the nodes in the network tend to connect to their connectivity peers, or disassortative mixing if nodes with low degrees are more likely to connect with high-degree nodes. We have known that biological networks such as protein–protein interaction networks (PPI), gene regulatory networks, and metabolic networks tend to be disassortative. On the other hand, in biological evolution, duplication and divergence are two fundamental processes. In order to make the relationship between the property of disassortative mixing and the two basic biological principles clear and to study the cause of the disassortative mixing property in biological networks, we present a random duplication model and an anti-preference duplication model. Our results show that disassortative mixing networks can be obtained by both kinds of models from uncorrelated initial networks. Moreover, with the growth of the network size, the disassortative mixing property becomes more obvious.

On the asymptotic behavior of hopfield neural network with periodic inputs

Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhins coincidence degree theory and Liapunovs function method.

The matric algorithm of Lyapunov exponent for the experimental data obtained in dynamic analysis

The Lyapunov exponent is important quantitative index for describing chaotic attractors. Since Wolf put up the trajectory algorithm to Lyapunov exponent in 1985, how to calculate the Lyapunov exponent with accuracy has become a very important question. Based on the theoretical algorithm of Zuo Binwu, the matric algorithm of Lyapunov exponent is given, and the results with the results of Wolfs algorithm are compared. The calculating results validate that the matric algorithm has sufficient accuracy, and the relationship between the character of attractor and the value of Lyapunov exponent is studied in this paper. The corresponding conclusions are given in this paper.

Threshold value for diagnosis of chaotic nature of the data obtained in nonlinear dynamic analysis

In this paper surrogate data method of phase-randomized is proposed to identify the random or chaotic nature of the data obtained in dynamic analysis. The calculating results validate the phase-randomized method to be useful as it can increase the extent of accuracy of the results. And the calculating results show that threshold values of the random timeseries and nonlinear chaotic timeseries have marked difference.

The concave or convex peaked and smooth soliton solutions of Camassa-Holm equation

The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa-Holm equation are studied. The concept of concave or convex peaked soliton and smooth soliton were introduced. And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson. Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.