THE PERIODIC HOLLING Ⅱ PREDATOR-PREY MODEL WITH IMPULSIVE EFFECT

In this paper, a periodic Holling II predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation, some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

1.IntroductionGopalsamyandLadajs[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,T20.Ifa>0,b<0andc=0,then(1.1)reducestotheLogisticequation.Ifb>0,(l.1)exhibitstheso--calledAlic...     

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.     

PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION

Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.     

ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE N-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.     

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

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

Existence and Stability for Periodic Solution of Competition Reaction－Diffusion Models with Grazing Rates in Population Dynamics

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Existence and Stability for Periodic Solution of Cooperation Ecosystem with Diffusion

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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.     

TIME-DEPENDENT COOPERATIVE SYSTEM OFPOPULATION GROWTH

*ThisresearchissupportedbytheNationalNaturalScienceFOundationofChina.1.IntroductionThevastmajorityofmathematicalmodelswhichhavebeenusedintheoreticalecologytostudythedynamicsofpopulationgrowthareautonomous.Thatistosaystheyattempttodescribethegrowthandinteractionofspecieswithconstantvitalparameterslivinginaconstantenvironment.Whilethishypothesisofconstantenvironmentandvitalparametersisjustifiableundersomecircumstances,amorerealisticmodelwouldcertainlyallowforthetemporalvariationoftheseparamet…     

Periodic solution and persistence for a three-species ratio-dependent predator-prey model with time delays in two-patch environments*

The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.     

A delayed ratio-dependent predator-prey system with stage-structured and impulsive effect

In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable.     

A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING*

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.     

UNIFORM PERSISTENCE IN DISCRETE SEMIDYNAMICAL SYSTEM AND ITS APPLICATION

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PERIODIC SOLUTIONS AND GLOBAL ASYMPTOTIC STABILITY OF A DELAYED DISCRETE PREDATOR-PREY SYSTEM WITH HOLLING II TYPE FUNCTIONAL RESPONSE

In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Hoffing Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.     

Existence and Stability of Positive PeriodicSolution of Delay Logistic Ecosystem with Feedback Control and Diffusion

1IntroductionWeconsiderthedelaylogisticecosystemwithfeedbackcontrolanddiffusionoftheformConcerningthestabilityproblemofpositivestead-stateforsystem(1.1),ithasbeendiscussedbyX.Shengli[1],whereastheasymptoticbehaviorofsolutionsofsystem(1.1)withoutdiffusionhasalsobeenconsideredbyK.Gopalsamy[2]andtheoscillationofsystem(1.1)withoutdiffusionandfeedbackcontrolcanbefoundinreference[3](K.GopalsamyandG.Ladas),Inreference[4],J.Dangpinghasgivedsufficientconditionsofexistenceandstabilityofperiodicsolut…     

ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

1.IntroductionConsiderthefollowinggeneralizedLi6nardtypeequationwhereshallowing[1],thisequationwillbecalledasaLi6nard-typeequationofordern.Whenn=1,theequation(1.1)canbewrittenasthefollowingformClearly)whenfi(x)=j(x),f200=0,theequation(1.3)isreducedtothewellknownLi6nardequationx j(x)x g(x)=0.(1.4)Recently,theequation(1.3)hasalreadybeenstudiedwithparticularemphasisontheex-istenceanduniquenessofperiodicsolutionsbyseveralauthors.Forexample,needmanandKuangll],GuidorizzilZ],ZhouJinI3],andJiangJ…     

定期保障策略下远航舰艇备件瞬时短缺数评估模型

定期保障条件下远航舰艇备件保障方案规划是海军装备保障工作的重大课题,目前尚未出现有效的解决方法。分析了远航舰艇定期备件保障系统和保障流程,提出了备件瞬时短缺数的定义和数学模型,根据远航舰艇定期保障中自我保障阶段、定期初始保障阶段和定期循环保障阶段的特点,建立了远海舰艇备件定期保障备件瞬时短缺数概率分布模型。最后,通过实例分析,输出结果表明模型能够反映远航舰艇定期保障备件瞬时短缺数的变化规律,可为装备保障指挥人员备件方案决策提供支持。     

具分布延时细胞神经网络的指数周期与稳定性

研究了具分布延时细胞神经网络的全局指数周期性与指数稳定性。在没有假设激活函数是有界的、可微的、单调增的情况下,通过应用一些新的分析技巧与Halanay-type不等式方法,得到了确保延时细胞神经网络周期解存在唯一且全局指数周期与全局指数稳定的简单的、容易验证的、新的充分条件。并给出了算例及其仿真结果支持所得结论。     

从形式结构看辩证法的系统维度

辩证法与系统论的结合，不仅可以从系统论走向辩证法，也可以从辩证法走向系统论。如果把否定之否定规律作为出发点并进行适度抽象而予以形式化，那么，否定之否定过程的“三段式”模式就表现为一个以环节为其结构成分的周期链。以辩证否定的原则来解读这个周期链，可以发现其中隐藏了无数种变易的可能性，“三段式”周期性结构只是其中的一种典型表达式而不是唯一的表达式。事实上，否定之否定的过程是一个具有复杂性维度的系统过程。