三次系统存在一类双纽线分界线环充要条件

给出了中心对称三次系统存在一类双纽线分界线环的充要条件，并举出此系统至少还存在四个极限环的（2．2）分布的例子．还举出了中心对称三次系统至少存在六个极限环作（3.3）分布以及五个极限环，其中一个极限环包围作（2．2）分布的四个极限环的例子．     

一类Leslie模型的定性分析

对一类Leslie模型进行定性分析，研究了其极限环的存在性，不存在性和唯一性．证明了该系统在细焦点外围至多有一个极限环，以及如果系统有奇数个极限环，则它恰有一个极限环．     

一类平面五次系统的极限环

研究了一类生化反应模型得到了极限环不存在或存在唯一的如下条件：１）若Ｐ＜０，则系统（１）存在唯一稳定的极限环．２）若Ｐ≥０．则系统（１）不存在极限环．     

一类具有二阶细焦点的二次系统

文[2]已经证明,具有三阶细焦点的二次系统(叶彦谦形式)当n=0时不存在极限环。本文继续运用文[2]的方法,得到了具有二阶细焦点的二次系统当n=0时在二阶细焦点外围存在极限环的条件和不存在极限环的条件,同时证明这种系统在其他奇点外围不存在极限环。     

一类平面七次多项式系统赤道环的稳定性与极限环分支

本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支，给出了系统的前12个奇点量公式，可积性条件及在赤道附近存在3个极限环的条件，较为精细地指出了极限环的存在位置。     

微分方程组=a+sum from ((i+j)=2) (a_(ij)x~iy~j),=b+sum from ((i+j)=2) (b_(ij)x~iy~j)的极限环存在的分歧值与代数奇异环

§1 引言 董金柱最先研究如下的二次系统[1]: (?)=α+sum from i+j=2 (α_(ij)x~iy~i,(?)=b+sum from i+j=2 (b_(ij)x~iy~i) (E) 的极限环的个数问题,他指出(E)可以至少存在两个极限环,且这两个极限环的位置分布在两个奇点周围。文[2]中证明了(E)至多存在两个极限环。本文将应用旋转向量场理论,研究当旋转参数α=时极限环变为奇异环的分歧值。从而得出一些情况下(E)恰存在两个极限环的充要条件。依据[2],研究(E)的极限环,只要研究如下系统就行了:     

具Holling I型功能反应的食铒——捕食系统的极限环

本文研究一类食铒——捕食的生态系统(1)在域R:{(x,y)|x≥0,y≥0}内的全局稳定性和极限环的存在性,给出了正平衡点全局渐近稳定的条件,存在两个极限环的条件。本文还估计了极限环的位置,用计算机绘制两个极限环的相图和计算了一些存在半稳定环的分岐值。 本文除了在集合存在半稳定环的具体分岐值以及极限环的唯二性证明未考虑外,其它的分岐值都已考虑,参数变动是大范围的。本文的推论包含了文[2,3]的结果。     

(En)系统极限环的相对位置

本文证明了,对任意正整数K,存在平面n次系统,它具有一串不少于K个大极限环.这些大极限环两两之间各有若干小极限环.     

(En)系统极限环的相对位置

本文证明了，对任意正整数K，存在平面n次系统，它具有一串不少于K个大极限环．这些大极限环两两之间各有若干小极限环．     

一类三次系统极限环的惟一性

讨论三次系统x=x(A0+A1x+A2y+A3xy-A4y2)y=y(x-1)的极限环问题.得到了该系统不存在极限环和存在惟一极限环的条件.     

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.     

Robust tube-based MPC of constrained piecewise affine systems with bounded additive disturbances

In this article, we propose a robust tube-based MPC formulation for a class of hybrid systems, namely autonomously switched PWA systems, with bounded additive disturbances. The term tube-based refers to those control techniques whose objective is to maintain all possible trajectories of the uncertain system inside a tube which is a set around the nominal (or reference) system trajectory, that is free from disturbances. Common methods in tube-based control systems consider an error dynamical system as the difference between the state of the nominal system and the state of the perturbed system. However, this definition of the error dynamical system leads to a complicated switched affine system for PWA systems. Therefore, we use a new notion of the reference system similar to the nominal system except that the switching between the various modes of the PWA system is driven by the state of the real system. Using this reference system instead of the nominal system leads us to an error dynamical system that can be modeled as a switched linear system. We employ a switched linear controller to stabilize this error system under arbitrary switching. This auxiliary controller forces the states of the uncertain system to remain in a tube confined to the invariant set around the state of the reference system. We add new constraints and tighten some other constraints of the nominal hybrid MPC for the reference system, in order to ensure convergence of the uncertain system and to guarantee robust exponential stability of the closed-loop system.     

Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response

In this paper, we discuss a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we investigate the asymptotic behavior of this system. When the white noise is small, the stochastic system imitates the corresponding deterministic system. Either there is a stationary distribution, or the predator population will die out. While if the white noise is large, besides the extinction of the predator population, both species in the system may also die out, which does not happen in the deterministic system. Finally, simulations are carried out to conform to our results.     

加权演化的港口网络模型的研究

港口系统的发展、演化对国民经济的繁荣发展起着至关重要的作用,因此如何定量地描述港口系统的发展、演化规律也就显得尤为关键,由此出发,从整体论的角度把港口系统作为一个整体来进行系统研究,利用复杂网络的特性,提出了一个真实的随时间演化的港口系统发展、演化模型,该模型能够有效地再现实际港口系统的一些统计特性,这些特性对于了解港口系统的运行状态和对于港口容错能力的优化将具有十分重要的意义.     

Canonical form of a nonlinear monetary system

This paper addresses an autonomous system of quadratic ordinary differential equations, which describes a monetary system involving interest rate, investment demand and price index. The canonical form of this system is derived, which is dependent on a single parameter. On this basis, it is proved that this system is not smoothly equivalent to the generalized Lorenz canonical form.     

F—fuzzy演绎系统

本文建立了一种演绎系统FFCS,在该演义系统中可以处理具有模糊性的推理过程,区别与其他对模糊推理进行形式化的逻辑系统,FFCS对模糊假言推理FMP做了完全形式化的处理。     

货币供给动态调控模型及其稳定性

根据我国货币政策传导机制并结合目前经济金融形势,建立了货币供给系统的一般动态模型,为了便于分析系统的稳定性,在此基础上建立前向离散货币供给系统简化模型并用经济控制论的方法分析了系统的稳定性。     

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.     

Poisson冲击下的$k/n(G)$系统的可靠性分析

本文研究了一类Poisson冲击下的$k/n(G)$系统(即$k$-out-of-$n$: $G$系统). 假定冲击的到达数形成一个参数为$\lambda$的Poisson过程, 且冲击的量服从某一分布. 当每次冲击到达时, 对系统中工作的部件独立地产生影响. 进而假定每一部件以一定的概率故障, 概率值是冲击量的函数. 且各次冲击独立地对系统造成损失, 直到工作部件数少于$k$系统故障为止. 在这些假定下, 我们获得了系统的可靠度函数和系统的平均工作时间. 进一步, 假定系统是可修的, 系统中有一个维修工, 并根据``先坏先修’’的维修规则对故障部件进行维修. 在维修时间服从指数分布的假设下, 系统状态转移服从Markov过程. 对该系统我们建立了状态转移方程, 并求得了系统可用度、稳态下的平均工作时间、平均停工时间和系统失效频率等可靠性指标. 最后, 我们还给出了一个简单例子来演示讨论的模型.     

An Example of (3+1)-Dimensional Integrable System

In this paper an example of the (3+1)-dimensional integrable system is considered and the infinite series of divergent forms are described. The classical symmetries for this system, the factor-equation for these symmetries, and exact solutions of this system are found.