A single-server discrete-time queue with correlated positive and negative customer arrivals

An MMBP/Geo/1 queue with correlated positive and negative customer arrivals is studied. In the infinite-capacity queueing system, positive customers and negative customers are generated by a Bernoulli bursty source with two correlated geometrically distributed periods. I.e., positive and negative customers arrive to the system according to two different geometrical arrival processes. Under the late arrival scheme (LAS), two removal disciplines caused by negative customers are investigated in the paper. In individual removal scheme, a negative customer removes a positive customer in service if any, while in disaster model, a negative customer removes all positive customers in the system if any. The negative customer arrival has no effect on the system if it finds the system empty. We analyze the Markov chains underlying the queueing systems and evaluate the performance of two systems based on generating functions technique. Some explicit solutions of the system, such as the average buffer content and the stationary probabilities are obtained. Finally, the effect of several parameters on the system performance is shown numerically.     

Positive periodic solution for a neutral delay competitive system

In this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay. Applying the continuation theorem of coincidence degree theory, a general criteria on the existence of positive periodic solutions are established. Some the related results are generalized and improved. It is shown that the arguments delays have no effect on the existence positive periodic solution of system.     

A competition un-stirred chemostat model with virus in an aquatic system

A reaction–diffusion system of two bacteria species competing a single limiting nutrient with the consideration of virus infection is derived and analysed. Firstly, the well-posedness of the system, the existence of the trivial and semi-trivial steady states, and some prior estimations of the steady states are given. Secondly, a single species subsystem with virus is studied. The stability of the trivial and semi-trivial steady states and the uniform persistence of the subsystem are obtained. Further, taking the infective ability of virus as a bifurcation parameter, the global structure of the positive steady states and the effect of virus on the positive steady states are established via bifurcation theory and limiting arguments. It shows that the backward bifurcation may occur. Some sufficient conditions for the existence, uniqueness and stability of the positive steady state are also obtained. Finally, some sufficient conditions on the existence of the positive steady states for the full system are derived by using the fixed point index theory. Some results on persistence or extinction for the full system are also obtained.     

信息披露制度、公司风险投资(CVC)信息披露与公司价值

信息披露制度对信息披露水平的影响及其经济效果一直是学术研究的热点。在交易所信息披露制度文件基础上,本文构建了可靠的CVC信息披露水平指数。研究发现信息披露制度的出台有效地提高了CVC信息披露水平。利用信息披露制度出台这一准自然实验,采用双重差分法发现CVC信息披露水平的提高增加了上市公司价值,进一步研究发现不确定性和市场竞争程度会对二者关系产生调节作用。该研究结果说明信息披露制度具有积极的政策效用,也为CVC信息披露制度的出台提供了经验证据。     

On the perron sign change effect for Lyapunov characteristic exponents of solutions of differential systems

The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with small second-order perturbations, which realizes only a partial Perron effect.     

Cross-diffusion induced Turing instability for a three species food chain model

In this paper, we study a strongly coupled reaction–diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. We first show that the unique positive equilibrium solution is globally asymptotically stable for the corresponding ODE system. The positive equilibrium solution remains linearly stable for the reaction–diffusion system without cross-diffusion, hence it does not belong to the classical Turing instability scheme. We further proved that the positive equilibrium solution is globally asymptotically stable for the reaction–diffusion system without cross-diffusion by constructing a Lyapunov function. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction–diffusion system, hence the instability is driven solely from the effect of cross-diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions.     

一类具有比率和单调功能反应的中立型捕食系统的正周期解

研究了一类具有比率和单调功能反应的中立型捕食系统.通过利用重合度理论获得了其正周期解存在性的充分条件,推广和改进了已有文献的相关结果.     

Continual Version of the Perron Effect of Change in Values of Characteristic Exponents

A nonlinear perturbed differential system with a linear approximation is considered. An open question has been the validity of a (continual) version of the Perron effect when the set of Lyapunov exponents of all nontrivial solutions (necessarily infinitely extendable on the right) of the corresponding nonlinear perturbed system with a perturbation of arbitrary higher order of smallness in a neighborhood of the origin is measurable, lies entirely on the positive half-line, and has the cardinality of the continuum and even a positive Lebesgue measure. The positive answer to this question is given by the presented theorem, which generally determines an explicit representation of the Lyapunov exponents of all nontrivial solutions to the nonlinear system in terms of their initial values.     

国有企业人力资本与所有权安排的实证分析

本首先对中国国有企业人力资本与所有权安排制度作一简要考察，然后对中国国有企业人力资本与所有权安排问题进行实证分析，在此基础上进一步对国有企业人力资本与所有权安排的制度进行分析。     

Positive solutions for Lotka–Volterra competition system with large cross-diffusion in a spatially heterogeneous environment

In this paper, we study the stationary problem for the Lotka–Volterra competition system with cross-diffusion in a spatially heterogeneous environment. Although some sufficient conditions for the existence of positive solutions are obtained by using global bifurcation theory, the information for their structure is far from complete. In order to get better understanding of the competition system with cross-diffusion, we focus on the asymptotic behaviour of positive solutions and derive two shadow systems as the cross-diffusion coefficient tends to infinity, moreover, the structure of positive solutions of the limiting system is analysed. The result of asymptotic behaviour also reveals different phenomena from that studied in Wang and Li (2013).     

Asymptotics of regularized solutions of a linear nonautonomous system of advanced differential equations

For a nonautonomous system of linear advanced differential equations, we find asymptotic formulas analytically determining how the regular solutions of this system on an interval of the positive half-line depend on the admissible error. The problem is solved in the following setting: additional smoothness conditions are imposed on the initial functions, but the boundary conditions providing a continuous extension of the solutions of the Cauchy problem to an interval of the positive half-line are violated.     

Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions

The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an age-structured predator–prey system with spatial dispersion. Based on unilateral global bifurcation methods for Fredholm operators and on maximal regularity for parabolic equations, global bifurcation of positive solutions is derived.     

Local Exact Boundary Synchronization for a Kind of First Order Quasilinear Hyperbolic Systems

In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a uniform constructive method is adopted, rather than an iteration process usually used in dealing with nonlinear systems. Furthermore, similar results on the exact boundary synchronization by groups can be obtained for a kind of first order quasilinear hyperbolic system of equations with different positive wave speeds by groups.     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

Periodic solutions of neutral functional differential systems with two parameters

In this paper, we consider certain first-order neutral differential system with two parameters. Some existence results of one positive periodic solution and two positive periodic solutions and nonexistence of positive periodic solutions are obtained. Our approach is based on Krasnoselskii fixed point theorem in cones.     

STABILITY ANALYSIS OF A LOTKA-VOLTERRA COMMENSAL SYMBIOSIS MODEL INVOLVING ALLEE EFFECT

In this paper, we present a stability analysis of a Lotka-Volterra commensal symbiosis model subject to Allee effect on the unaffected population which occurs at low population density. By analyzing the Jacobian matrix about the positive equilibrium, we show that the positive equilibrium is locally asymptotically stable. By applying the differential inequality theory, we show that the system is permanent, consequently, the boundary equilibria of the system is unstable. Finally, by using the Dulac criterion, we show that the positive equilibrium is globally stable. Although Allee effect has no influence on the final densities of the predator and prey species, numeric simulations show that the system subject to an Allee effect takes much longer time to reach its stable steady-state solution, in this sense that Allee effect has unstable effect on the system, however, such an effect is controllable. Such an finding is greatly different to that of the predator-prey model.     

Existence and Uniqueness of Positive Radial Solutions for a Class of Quasilinear Elliptic Systems

This article is concerned with the existence and uniqueness of positive radial solutions for a class of quasilinear elliptic system. With some reasonable assumptions on the nonlinear source functions and their coefficients, the existence and the upper and lower bounds of the positive solutions will be provided by using the fixed point theorem and the maximum principle for the quasilinear elliptic system.     

一类具有收获率的脉冲Lotka-Volterra竞争合作系统的八个正概周期解

研究了一类具有收获率的脉冲Lotka-Volterra竞争合作系统的正概周期解.通过利用重合度理论延拓定理、概周期理论和不等式分析技巧,获得了系统至少存在8个正概周期解的充分条件,推广和改进了早期文献的相关结果.     

三维Lotka-Volterra 系统正拟周期解的存在性和稳定性

This work focuses on the existence and stability of positive quasi-periodic solutions for the 3-dimensional Lotka-Volterra system. Using KAM （Kolmogorov-Arnold-Moser） theory and Newton iteration, it is shown that there exists a positive quasi-periodic solution in a Cantor family for the 3-dimensional Lotka-Volterra system. On the above basis, we can show the stability of the solution with the help of Lyapunov function.     

一类具第三类功能反应且食饵具有避难所的捕食系统的分析

研究了一类具第三类功能反应且食饵具有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下,系统存在全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.