PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

一类广义半无限规划问题的光滑牛顿算法

本文在广义半无限规划问题的最优解集X处满足某些条件的前提下将广义半无限规划问题转化成KKT系统,通过扰动的FB函数,将KKT系统转化为一组光滑函数方程,设计了一个光滑牛顿算法,证明了算法的全局收敛性,并且在光滑函数解集处满足局部误差界条件下证明了算法具有超线性收敛速率.     

Boundary feedback control of elastic beam equation with structural damping and stability

In this paper, we consider the partial differential equation of an elastic beam with structural damping by boundary feedback control. First, we prove this closed system is well-posed; then we establish the exponential stability for this elastic system by using a theorem whichbelongs to F. L. Huang^[2]; finally, we discuss the distribution and multiplicity of the spectrum of this system. These results are very important and useful in practical applications.     

时滞Lotka-Volterra系统的持久性和周期解

本文研究具有时滞周期捕食系统的持久性和周期解,得到了系统永久持续生存的充要条件。在此条件下系统存在正的ω周期解,改进了一些已知结果。     

On the Cauchy problem of a two-component b-family system

In this paper, we study the Cauchy problem of a two-component b-family system. We first establish the local well-posedness for a two-component b-family system by Kato’s semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the system. Moreover, we present several blow-up results for strong solutions to the system.     

Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities

In this paper, we study a non-local coupled system arising in the modeling of the dynamics of dislocation densities in crystals. For this system, the global existence and uniqueness are available only for continuous viscosity solutions. In the present paper, we investigate the global time existence of this system by considering BV initial data. Based on a fundamental uniform BV estimate and the finite speed of propagation property of this system, we show, in a particular setting, the global existence of discontinuous viscosity solutions of this problem.     

Hilbert空间中关于松弛协强制映射的一类新的广义变分不等式组

在本文中,我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组,通过用度量投影的方法,我们证明了这类广义变分不等式组解的存在性和唯一性.我们也建立了一类新的算法来逼近这一不等式组的解,本文的结果使得近期相关结果成为本文的特殊情况.     

On the linearization of isochronous centre of a modified Emden equation with linear external forcing

In this work, we carry out a detailed study on the linearization of isochronous centre of a modified Emden equation with linear external forcing. We construct inverse integrating factor and time independent first integral for this system through Darboux method. To linearize the isochronous centre we explore a transverse commuting dynamical system and its first integral. With the help of first integrals of the original dynamical system and its transverse commuting system we derive the linearizing transformation and reduce the nonlinear system into linear isochronous one. We also point out certain mathematical structures associated with this dynamical system.     

THE EXISTENCE AND STABILITY OF THE HETEROCLINIC CYCLE IN A KIND OF BIOLOGICAL SYSTEM

IIntroductlonConsider the n－spedes biological systemlit\1．＝IJ!厂．＋》*i,工上D、忍＝上,’··。n．ti)Ifffi＝1,it is S S－SpSCllS LOthaka－VoltOOYY SystSS．Iftti＝2,It Is S S－sPeCieSKolmongorov system．As to the n－spedes Gause－Lotb－Volterra system矿ti 乙工．＝T;Ii、y Qiil．I。Ti 7 U,on M U,t6)174 AnnofDiff Eqs．VO18M叫 and Leonard[1],Ho凡aner and Sigmund问 have studied this system forthe case n二 3 respectlvelyand noted that thereprobably exists aheterocllnlccyclefor…     

Necessary-Sufficient Conditions for Permanence and Extinction in Lotka-Volterra System with Discrete Delays

In this article, we give the necessary and sufficient conditions for permanence and extinction of a two-species Lotka-Volterra system with different discrete delays. We improve some previous results. Moreover, we show the permanence and extinction for this system is equivalent to that of its corresponding nondelayed system.     

Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

     

Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces

In this article, we introduce and consider a general system of variational inequalities. Using the projection technique, we suggest and analyse new iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving the single operator, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results improve and extend the recent ones announced by many others.     

逐步删除法确定复杂系统主导结构及其应用

在流率基本入树建模法、反馈环行列式计算法和系统基模X-0-1行列式计算法的基础上,结合系统行为模拟分析的变化曲线,提出了确定系统关键变量主导结构的逐步删除法,为复杂系统的动态结构和行为模式的分析提供有效的方法.运用此方法,对"公司+农户"规模经营模式的系统关键变量主导结构进行了分析,并提出相应的管理方针,实现了用系统科学方法分析"三农"问题的目的.     

A LOTKA-VOLTERRA PREY-PREDATOR SYSTEM WITH FEEDBACK CONTROL EFFECT

In this paper, we propose a Lotka-Volterra prey-predator system with discrete delays and feedback control. Firstly, we show that solution of the system is bounded. Secondly, we obtain sufficient condition for the global stability of the unique positive equilibrium to the system.     

多服务台可修排队的稳态分布存在条件

本文分析多服务台可修排队系统的稳态分布存在条件。多服务台可修排队系统可利用拟生灭过程理论处理。拟生灭过程方法给出了矩阵形式的多服务台可修排队系统的稳态分布存在条件。本文由这一矩阵形式的稳态分布存在条件导出具有明显概率意义的稳态分布存在条件的另一种形式，从而证明了两种不同形式的稳态分布存在条件的一致性。     

The equiconvergence of expansions in eigenfunctions and associated functions of an integral operator with involution

In this paper we study an integral operator with involution. We solve the problem on the exact inversion of this operator, we obtain and study the integro-differential system for the Fredholm resolvent and, finally, we prove the theorem on the equiconvergence of expansions in eigenfunctions and associated functions, in the usual trigonometric system.     

A fast Petrov–Galerkin method for solving the generalized airfoil equation

In this paper we develop a fast Petrov–Galerkin method for solving the generalized airfoil equation using the Chebyshev polynomials. The conventional method for solving this equation leads to a linear system with a dense coefficient matrix. When the order of the linear system is large, the computational complexity for solving the corresponding linear system is huge. For this we propose the matrix truncation strategy, which compresses the dense coefficient matrix into a sparse matrix. We prove that the truncated method preserves the optimal order of the approximate solution for the conventional method. Moreover, we solve the truncated equation using the multilevel augmentation method. The computational complexity for solving this truncated linear system is estimated to be linear up to a logarithmic factor.     

Priority centralization of the one period multi-location inventory system

In this paper, we will examine a multi-center one-period inventory system. The usual penalty cost for being out of stock will be replaced by an assurance of service constraint at each location. That is, we will constrain our inventory size to meet a specific maximum probability of being out of stock at each location. The centralized system we shall propose will define a priority rule which will cause us to satisfy the entire demand of high priority locations before we begin satisfying the demands of lower priority locations. This will allow us to find a minimum initial inventory level for the centralized system that will meet all of the assurance of service constraints. We will look at the special case where the variance of the total demand of several locations is non-decreasing in locations included in the total. In this case, we will show the computations required for finding the optimal centralized priority system are minimal. Finally, we will show that such a system is superior to a decentralized system.     

一类捕食者-食饵系统的全局结构

本文中我们证明了关于一般捕食者-食饵系统不存在闭轨线的定理,即文中定理2.应用这一定理和关于捕食者-食饵系统极限环的存在唯一性定理[1],我们完成了在各种参数条件对一个具体的捕食者-食饵系统模型[2]的研究.     

Existence of Solutions to a Generalized System

In this paper, we consider a generalized system in real Banach spaces. Using Brouwer’s fixed-point theorem, we establish some existence theorems for generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity for a bifunction and extend Minty’s lemma for a generalized system. Furthermore, using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for a generalized system with monotonicity in real reflexive Banach spaces.