This paper studies the human behavior in the top-one social network system in China (Sina Microblog system). By analyzing real-life data at a large scale, we find that the message releasing interval (intermessage time) obeys power law distribution both at individual level and at group level. Statistical analysis also reveals that human behavior in social network is mainly driven by four basic elements: social pressure, social identity, social participation, and social relation between individuals. Empirical results present the four elements' impact on the human behavior and the relation between these elements. To further understand the mechanism of such dynamic phenomena, a hybrid human dynamic model which combines “interest” of individual and “interaction” among people is introduced, incorporating the four elements simultaneously. To provide a solid evaluation, we simulate both two-agent and multiagent interactions with real-life social network topology. We achieve the consistent results between empirical studies and the simulations. The model can provide a good understanding of human dynamics in social network.

We propose an approach for structural learning of directed acyclic graphs from multiple databases. We first learn a local structure from each database separately, and then we combine these local structures together to construct a global graph over all variables. In our approach, we do not require conditional independence, which is a basic assumption in most methods.

This paper is concerned with the regular dynamic loop-like subdivision scheme based on the extension of Box-Spline method. The purpose of the addressed problem is to prove the convergence of the subdivision scheme and verify the $C^0$ and $C^1$ continuity by calculating the eigenvalues of the 2-neighbor subdivision matrix. Compared with the loop subdivision scheme in previous references, the designed scheme can generate exact revolving surfaces and hold a stronger modeling capability because the subdivision matrix can update regularly with the iteration procedure. Finally, some examples are given to illustrate the effectiveness of the proposed method.

This paper further studies the $p$th moment exponential stability of stochastic pulse-width-modulated (PWM) feedback systems with distributed time-varying delays. We establish several globally exponential stability criteria for such PWM feedback systems by using Lyapunov-Krasovskii functional and then present an upper bound of the parameter of PWM when the system is stable and such system has stronger anti-interference performance than the system without time-varying delays. Furthermore, we present two examples to show the effectiveness and conservativeness of the theoretical results.

We present a linear backward Euler fully discrete finite volume method for the initial-boundary-value problem of purely longitudinal motion of a homogeneous bar and an give optimal order error estimates in $L^2$ and $H^1$ norms. Furthermore, we obtain the superconvergence error estimate of the generalized projection of the solution $u$ in $H^1$ norm. Numerical experiment illustrates the convergence and stability of this scheme.

We consider the systems of $(-1{)}^m{u}^{(2m)}=\lambda u+\lambda v+uf(t,u,v),t\in (\mathrm{0,1}),u^{(2i)}(0)=u^{(2i)}(1)=0$, and $0\le i\le m-1,(-1{)}^m{v}^{(2m)}=\mu u+\mu v+vg(t,u,v),t\in (\mathrm{0,1}),v^{(2i)}(0)=v^{(2i)}(1)=0,0\le i\le m-1$, where $\lambda ,\mu \in R$ are real parameters. $f,g:[\mathrm{0,1}]\times R^2\to R$ are $C^k,k\ge 3$ functions and $f(t,\mathrm{0,0})=g(t,\mathrm{0,0})=0,t\in [\mathrm{0,1}]$. It will be shown that if the functions, $f$ and $g$ are “generic” then the solution set of the systems consists of a countable collection of 2-dimensional, $C^k$ manifolds.

Air permeability in hierarchic porous media does not obey Fick's equation or its modification because fractal objects have well-defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first time, a seemingly complex air permeability process using fractal derivative method. The fractal derivative model has been successfully applied to explain the novel air permeability phenomenon of cocoon. The theoretical analysis was in agreement with experimental results.

Chaotic Neural Network, also denoted by the acronym CNN, has rich dynamical behaviors that can be harnessed in promising engineering applications. However, due to its complex synapse learning rules and network structure, it is difficult to update its synaptic weights quickly and implement its large scale physical circuit. This paper addresses an implementation scheme of a novel CNN with memristive neural synapses that may provide a feasible solution for further development of CNN. Memristor, widely known as the fourth fundamental circuit element, was theoretically predicted by Chua in 1971 and has been developed in 2008 by the researchers in Hewlett-Packard Laboratory. Memristor based hybrid nanoscale CMOS technology is expected to revolutionize the digital and neuromorphic computation. The proposed memristive CNN has four significant features: (1) nanoscale memristors can simplify the synaptic circuit greatly and enable the synaptic weights update easily; (2) it can separate stored patterns from superimposed input; (3) it can deal with one-to-many associative memory; (4) it can deal with many-to-many associative memory. Simulation results are provided to illustrate the effectiveness of the proposed scheme.

This paper further studies the moment stability of pulse-width-modulated (PWM) feedback system which is subjected to multiplicative and additive random disturbance modeled by the derivative of Wiener process. Different from the existing investigation, we focus on its critical case. The linear plant considered herein is assumed to be critically stable; that is, the plant has one and only one pole at the origin, and the rest of the poles are left half of complex plane. We establish several globally asymptotically stability criteria for such PWM feedback systems and then propose an algorithm to calculate the stability bound effectively. Furthermore, we present two numerical examples to show the effectiveness of the theoretical results.

Over the last three decades, theoretical design and circuitry implementation of various chaotic generators by simple electronic circuits have been a key subject of nonlinear science. In 2008, the successful development of memristor brings new activity for this research. Memristor is a new nanometre-scale passive circuit element, which possesses memory and nonlinear characteristics. This makes it have a unique charm to attract many researchers’ interests. In this paper, memristor, for the first time, is introduced in a delayed system to design a signal generator to produce chaotic behaviour. By replacing the nonlinear function with memristors in parallel, the memristor oscillator exhibits a chaotic attractor. The simulated results demonstrate that the performance is well predicted by the mathematical analysis and supports the viability of the design.

Different from the most existing results, in this paper an intermittent control scheme is designed to achieve lag synchronization of coupled hyperchaotic systems. Several sufficient conditions ensuring lag synchronization are proposed by rigorous theoretical analysis with the help of the Lyapunov stability theory. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

This paper studies the problem of guaranteed cost control for a class of uncertain delayed neural networks. The time delay is a continuous function belonging to a given interval but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control, and new sufficient conditions for the existence of the guaranteed cost state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Nowadays, multi-agent networks are ubiquitous in the real world. Over the last decade, consensus has received an increasing attention from various disciplines. This paper investigates cluster consensus for discrete-time multi-agent networks. By utilizing a special coupling matrix and the Kronecker product, a criterion based on linear matrix inequality (LMI) is obtained. It is shown that the addressed discrete-time multi-agent networks achieve cluster consensus if a certain LMI is feasible. Finally, an example is given to demonstrate the effectiveness of the proposed criterion.

This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.