Hopf bifurcation analysis in a fluid flow model of Internet congestion control algorithm

This paper focuses on the Hopf bifurcation analysis of some classes of nonlinear time-delay models, namely fluid flow models, for the Internet congestion control algorithm of TCP/AQM networks. Using tools from control and bifurcation theory, it is proved that there exists a critical value of communication delay for the stability of the network. When the delay passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the stability of the bifurcation and direction of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical examples are given to verify the theoretical analysis.     

Exact algorithms for a selective Vehicle Routing Problem where the longest route is minimized

In this paper, we study a non-capacitated Vehicle Routing Problem (VRP) where not necessarily all clients need to be visited and the goal is to minimize the length of the longest vehicle route. An Integer Programming Formulation, a Branch-and-cut (BC) method and a Local Branching (LB) framework that uses BC as the inner solver are presented. Sharper upper bounds are obtained by LB, when the same time limit was imposed on the execution times of both approaches. Our results also suggest that the min-max nature of the objective function combined with the fact that not all vertices need to be visited make such problem very difficult to solve.     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals＇ relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each ease. Finally, we present numerical simulations for each case to verify our results.     

一类二阶多点边值问题正解的存在性

利用锥上不动点定理讨论了二阶常微分方程组多点边值问题正解的存在性，所得结论推广了最近的一些结果．     

Existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model

By means of the Cauchy matrix, we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population.     

General admissibility for linear estimators in a general multivariate linear model under balanced loss function

A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.     

Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays

In the current paper, BAM neural networks with time-varying coefficients and distributed time delays are studied. Sufficient conditions guaranteeing the exponential componentwise convergence and existence of one unique periodic solution are obtained by the comparison principle, continuation theorem of topological degree and inequality techniques. The boundedness and differentiability of activation functions are removed. The obtained sufficient criteria are easy to verify and are hence very useful in applications.