一类摄动系统的Poincare分叉与极限环

本文利用临界情形的隐函数存在定理讨论了一类摄动系统分支周期解的存在性与稳定性，利用后继函数法讨论了该系统极限环的存在性、唯一性和稳定性。     

具有一个高阶奇点和两个零特征根的一类多项式系统

本文讨论了具有一个高阶奇点和两个零特征根的一类２ｎ＋１次系统，证明了这类系统可以存在两个ｎ阶细焦点，给出极限存在性和不存在性的条件，并证明了无穷远分界线环的存在性。     

周期解的存在性、唯一性与稳定性

本文研究了高维周期系统的周期解的存在性、唯一性及稳定性等问题，利用指数型二分性和不动点方法，建立了保证周期解的存在性、唯一性及稳定性的充分条件，所得的结果推广了文［１、２］的主要结果。     

平面自治系统极限环的存在性

本文研究一般自治系统的极限环存在性问题，在一定条件下，我们证明该系统极限环的存在性，所得结果推广和改进了文［５—７］的相应结论．     

高维系统周期解的存在性与唯一性

本文首先利用一种新方法讨论高维系统解的一致有界性，一致最终有界性及非常稳定性问题，然后将所获结果应用于高维系统周期解的存在性与唯一性的研究。另外，本文还提出了“阶梯形系统”的概念，并对其建立了一种利用系统部分方程周期解存在性判定整个系统周期解存在性的方法。     

一个群体防卫捕-食系统的定性分析

该文对一个群体防卫捕一食系统进行了较全面的定性分析．讨论了分界线的相对位置，得到了极限环的存在性、唯一性以及分界线环的存在性，首次证明了群体防卫捕一食系统可以至少存在两个或三个极限环．     

一类非线性大系统的周期解

本文讨论了一类非线性大系统周期解的存在性． 利用指数型二分性和不动点方法，建立了保证周期解存在性的条件，所得结果推广了文［１］的主要结果．     

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．     

指数二分性与自治奇摄动系统的退化同宿分支

利用指数二分性理论和泛函分析方法，我们研究了自治奇摄动系统的同，异宿轨道的存在性，给出了高维奇摄动系统从退化系统分支出同异宿轨道的Ｍｅｌ－ｎｉｋｏｖ型函数。     

Ezeilo概周期解存在性定理的推广

本文利用指数型二分性理论讨论了一般高维概周期系统的概周期解的存在性和唯一性，所得结果推广了Ｅｚｅｉｌｏ的一个概周期解的存在性定理     

Generation and suppression of a new hyperchaotic nonlinear model with complex variables

In this paper, we introduce a new hyperchaotic complex Chen model. This hyperchaotic complex system is constructed by adding a complex nonlinear term to the third equation of the chaotic complex Chen system with consideration it’s all variables are complex. The new system is a 6-dimensional continuous real autonomous hyperchaotic system. The properties of this system including invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and hyperchaotic behavior are studied. Different forms of hyperchaotic complex Chen systems are constructed. We suppress the hyperchaotic behavior of our system via passive control method by using one complex controller. The hyperchaotic attractors of the new system are converted to its unstable trivial fixed point and tracked to its unstable non trivial fixed points and periodic orbits. Block diagrams of our system are designed by using Matlab/Simulink after and before the suppression process to ensure the validity of the analytical results.     

一类离散生态经济系统稳定性与分支研究

本文研究了一个离散生态经济模型的稳定性和分支问题.利用离散奇异系统理论,中心流形定理及Neimark-Sacker分支理论,得到了系统关于不动点的稳定性和Neimark-Sacker分支的有关结果,并与相应的连续模型进行对比分析.推广了文献[5]的结果.     

Bifurcation of limit cycles at the equator for a class of polynomial differential system

In this paper, center conditions and bifurcation of limit cycles from the equator for a class of polynomial system of degree seven are studied. The method is based on converting a real system into a complex system. The recursion formula for the computation of singular point quantities of complex system at the infinity, and the relation of singular point quantities of complex system at the infinity with the focal values of its concomitant system at the infinity are given. Using the computer algebra system Mathematica, the first 14 singular point quantities of complex system at the infinity are deduced. At the same time, the conditions for the infinity of a real system to be a center and 14 order fine focus are derived respectively. A system of degree seven that bifurcates 13 limit cycles from the infinity is constructed for the first time.     

Volterra series approximation for rational nonlinear system

Rational nonlinear systems are widely used to model the phenomena in mechanics, biology, physics and engineering. However, there are no exact analytical solutions for rational nonlinear system. Hence, the approximate analytical solutions are good choices as they can give the estimation of the states for system analysis, controller design and reduction. In this paper, an approximate analytical solution for rational nonlinear system is derived in terms of the solution of a polynomial system by Volterra series theory. The rational nonlinear system is transformed to a singular polynomial system with finite terms by adding some algebraic constraints related to the rational terms. The analytical solution of singular polynomial system is approximated by the summation of the solutions of Volterra singular subsystems. Their analytical solutions are derived by a novel regularization algorithm. The first fourth Volterra subsystems are enough to approximate the analytical solution to guarantee the accuracy. Results of numerical experiments are reported to show the effectiveness of the proposed method.     

Parameter estimation using dynamic optimization in limited nutrient-consumer hybrid dynamical systems

A limited nutrient consumer hybrid system which exhibits rich dynamics such as stability, instability and oscillatory characteristics is considered. The parameters that strongly influence the behavior of the system are identified and are estimated using the techniques of dynamic optimization. Two independent bio-control mechanisms are introduced into the system when the basic system exhibits instability characteristics. Values of the parameters representing these mechanisms are estimated at which the system stabilizes. Examples and simulations illustrate the main results.     

无限维关联系统的弦稳定性

对一类无限维关联系统引入弦稳定概念。系统弦稳定意谓着,当关联系统的初始状态为有界时,对任意时刻系统的状态也是有界的。本文将向量V函数法推广到无限维系统中,得到了关联系统渐近弦稳定的充分条件,克服了以前的方法在处理非线性系统的稳定性问题上的困难,扩大了系统稳定的参数范围。     

基于系统可靠性的组件综合重要度变化机理分析

重要度理论是一种重要的系统薄弱环节识别和评估方法,被广泛应用于系统可靠性设计优化、维修资源分配、维修决策以及风险分析等领域。本文以组件状态转移率为纽带,分析了组件综合重要度对系统可靠性的影响机理,识别对系统可靠性变化影响最大的组件,综合重要度评估了单位时间内系统可靠性的变化。首先给出综合重要度的定义;其次讨论系统可靠性的组件重要度表示方法;最后在串联和并联系统中,分析综合重要度随着组件状态转移率的变化机理。     

Real-coded genetic algorithm for system identification and controller tuning

This paper presents an application of real-coded genetic algorithm (RGA) for system identification and controller tuning in process plants. The genetic algorithm is applied sequentially for system identification and controller tuning. First GA is applied to identify the changes in system parameters. Once the process parameters are identified, the optimal controller parameters are identified using GA. In the proposed genetic algorithm, the optimization variables are represented as floating point numbers. Also, cross over and mutation operators that can directly deal with the floating point numbers are used. The proposed approach has been applied for system identification and controller tuning in nonlinear pH process. The simulation results show that the GA based approach is effective in identifying the parameters of the system and the nonlinearity at various operating points in the nonlinear system.     

L~*系统的一种改进系统L_0~*

研究了王国俊教授建立的模糊命题演算的形式演绎系统 L*以及在语义上相关的修正的 Kleene逻辑系统 W,W,Wk,给出了 L*系统的一种改进系统 L*0 ,并证明了二者之间的等价性 ,为形式演绎系统 L* 的研究和应用提供了一个有益的途径     

Analytic study of multiserver buffers with two-state Markovian arrivals and constant service times of multiple slots

In this paper, we study the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive at the system according to a two-state Markovian arrival process. The service times of the packets are assumed to be constant, equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating functions (PGF’s). Explicit expressions are obtained for the PGF’s of the system contents and the packet delay. From these, the mean values, the variances and the tail distributions of the system contents and the packet delay are calculated. Numerical examples are given to show the influence of various model parameters on the system behavior.