A PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE ENSO MECHANISM

A class of coupled system of the E1Nifio/La Nifio-Southern Oscillation (ENSO) mechanism is studied. Using the perturbed theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behavior of the solution for corresponding problem is considered. And it is pointed out that the solution tends to the corresponding attractor as t→∞.     

THE HOPF BIFURCATION DIRECTION OF A FOUR DIMENSIONAL ELECTRONIC NEURAL NETWORK SYSTEM

1.IntroductionCurrentlybifurcationtheoryiswidelyusedinmanymathematicalmodelsofvariousfieldssuchasbiologyjmechanics,medicalscience,managementofnaturalresourcesandthetheoryofneuralnetowrks.Inadifferentialdynamicalsystem,averyimportalltproblemistheexistencea…     

QUALITATIVE ANALYSIS FOR A THIRD-ORDER DIFFERENTIAL EQUATION IN A MODEL OF CHEMICAL SYSTEMS

In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separatedat a finite distance from each other;at the same time,a technique for studying theHopf bifurcation value is given.     

二次创新竞争模型与企业竞争战略分析

本文用二次创新竞争模型描述了技术输出方和技术引进方的二次创新竞争情形。分析了技术引进方的二次创新在市场竞争中“后发优势”的成因。指出必须摒弃传统的对引进一消化、吸收－创新的单纯技术和封闭系统观，而立足于引进技术与市场的结合，用开放系统中的二次创新竞争制定正确的竞争战略，在赢得市场竞争优势的同时，培养自言创新能力。     

THE EIGEN-PROBLEM AND PERIOD ANALYSIS OF THE DISCRETE-EVENT SYSTEM

In this paper we provide a sufficient and necessary condition for the eigenvalueand eigenvector of a general reducible matrix in a discrete-event system described by the“max”algebra,analyse the steady periodical performance of the system,and obtain ananalytic solution of the dynamic equation.We propose the conception of“order-d-(?)-block-periodical matrix”and obtain its sufficient and necessary condition and provide an algorithmof (?) matrix.     

GLOBAL ATTRACTIVITY OF POPULATIONMODELS WITH DELAYS AND DIFFUSION

In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch Ω and periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators. Some earlier results are extended to population models with delays and diffusion.     

OVERLOAD ANALYSIS OF MARKOVIAN MODELS

1.IntroductionandMotivationsInavarietyofapplications,oneneedstofindthesteady-statedistributionsoffiniteMarkovchainswithalargenumberofstates,forexample,aqueuingsystemwithalargebiberorabigwaitingroom.Forsuchasystem,thesteady-statedistributionalwaysedestsnomatterhowlargethebibersizeisandnomatterwhetherornotthesystemisoverloaded.Whenthesystemisnotoverloaded,onemayusethecorrespolldingmodelwithaninfinitebufferforanapproximation.Thismethodoftentakestheadvantageofasimplersollltionstructureoftheindnit…     

A NEW APPROACH ON IDENTIFICATION OF BOUNDARY PARAMETER FOR A TWODIMENSIONAL DIFFUSION SYSTEM

This paper presents a new approach of the boundary parameter identification of adiffusion system.The system model is governed by a two-dimensional parabolic problem,which involves an unknown boundary parameter.Identifiability of the boundary parameterand the new approach are discussed briefly,which show that the new approach can overcomenot only the ill-posedness of the nonlinear output least square method but also the difficultyof numerical computation of the nonlinear output least square estimate due to the existenceof the local minima of the performance functional,Finally,some numerical examples aregiven.     

一个类Lorenz系统的Hopf分岔分析及分岔控制

对一个新的类Lorenz系统的Hopf分岔行为及分岔控制问题进行研究。首先,通过分岔稳定性指标判定系统的分岔类型。然后,分别对系统施加线性和非线性控制器。在线性控制部分,根据Routh-Hurwitz原理,讨论了线性参数对分岔位置的影响;在非线性控制部分,利用Normal Form(规范形)方法求出系统的Hopf分岔规范式,并通过规范式系数讨论非线性参数对Hopf分岔类型及极限环幅值的影响。结果表明当非线性参数满足一定条件时,原系统的Hopf分岔类型可以被改变,并且在超临界情况下,极限环幅值会随着非线性参数的增加而增加。     

EXISTENCE AND ANALYTICAL APPROXIMATIONS OF LIMIT CYCLES IN A THREE-DIMENSIONAL NONLINEAR AUTONOMOUS FEEDBACK CONTROL SYSTEM

This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system. Based on three-dimensional Hopf bifurcation theorem, the existence of limit cycles is first proved. Then the homotopy analysis method （HAM） is applied to obtain the analytical approximations of the limit cycle and its frequency. In deriving the higher-order approximations, the authors utilized the idea of a perturbation procedure proposed for limit cycles＇ approximation in van der Pol equation. By comparing with the numerical integration solutions, it is shown that the accuracy of the analytical results obtained in this paper is very high, even when the amplitude of the limit cycle is large.