A global solution curve for a class of periodic problems,including the relativistic pendulum

Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of periodic solutions. Our approach is suitable for numerical computations, and in fact we present some numerically computed bifurcation diagrams illustrating our results.     

DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS

In this paper,we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays.In fact,the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution,which is also its derivative pseudo almost periodic.This results are without resorting to the theory of exponential dichotomy.Furthermore,by employing the suitable Lyapunov function,some delay-independent sufficient conditions are derived for exponential convergence.The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity.Lastly,two examples are given to demonstrate the validity of the proposed theoretical results.     

Global chaos in a periodically forced, linear system with a dead-zone restoring force

The Poincare mapping and the corresponding mapping sections for global motions in a linear system possessing a dead-zone restoring force are introduced through switching planes pertaining to two constraints. The global periodic motions based on the Poincare mapping are determined, and the eigenvalue analysis for the stability and bifurcation of periodic motion is carried out. Global chaos in such a system is investigated numerically from the unstable global periodic motions analytically determined. The bifurcation scenario with varying parameters is presented. The mapping structures of periodic and chaotic motions are discussed. The Poincare mapping sections for global chaos are given for illustration. The grazing phenomenon embedded in chaotic motion is observed in this investigation.     

具有粘弹性和热粘弹性方程组的全局周期吸引子

证明了具有粘弹性和热粘弹性方程组在Dirichlet边界条件下,对于任意的非自治时间周期受迫力,均具有唯一的指数吸引任何有界集的周期解,即全局周期吸引子.并且如果受迫力是自治的,则全局周期吸引子恰是系统唯一的指数吸引有界集的平衡解.     

Generalization of the Jurdjevic-Quinn theorem and stabilization of bilinear control systems with periodic coefficients: I

The Jurdjevic-Quinn theorem on the global asymptotic stabilization of the origin is generalized to nonlinear time-varying affine control systems with periodic coefficients. The proof is based on the Krasovskii theorem on the global asymptotic stability for periodic systems and the introduced notion of “commutator” for two vector fields one of which is time-varying. The obtained sufficient conditions for stabilization are applied to bilinear control systems with periodic coefficients. We construct a control periodic in t in the form of a quadratic form in x that asymptotically stabilizes the zero solution of a bilinear periodic system with a time-invariant drift.     

Landau-Lifshitz-Maxwell方程组整体光滑解存在唯一性

该文研究了一维具有周期初值Landau-Lifshitz-Maxwell方程的整体光滑解的存在唯一性.为得到一致先验估计,作者利用了|Z(x,t)|=1和{Z,Z_x,Z×Z_x}构成R~3的一组基的办法.     

一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

On the global dynamics of periodic triangular maps

This paper is an extension of an earlier paper that dealt with global dynamics in autonomous triangular maps. In the current paper, we extend the results on global dynamics of autonomous triangular maps to periodic non-autonomous triangular maps. We show that, under certain conditions, the orbit of every point in a periodic non-autonomous triangular map converges to a fixed point (respectively, periodic orbit of period p) if and only if there is no periodic orbit of prime period two (respectively, periodic orbits of prime period greater than p).     

周期Gompertz生态系统中的最优脉冲控制收获策略

以周期Gompertz系统为基础,讨论了周期变化的单种群生物资源的收获优化问题及种群的动力学性质.在单位收获努力量假设下,以最大可持续收获量为管理目标,确定了线性收获下的最优收获策略,获得了最优收获努力量、最大可持续收获及相应的最优种群水平的显示表达式,为自然资源的开发和利用提供了理论依据.     

Global dynamics of the periodic logistic system with periodic impulsive perturbations

This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions.     

具有Monod-Haldane功能反应和脉冲效应的捕食系统的动力学性质

基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件．并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟．     

弱分次周期根

对一般群分次环境立了弱分次周期根的概念,证明它是一个分次特殊根,给出了它的分次模刻,讲座了它与自反周期根的关系。     

一类具有饱和传染力的Schoner竞争系统的概周期解

对一类具有饱和传染力的Schoner竞争系统进行了研究,得到了系统持久生存和任一正解全局渐近稳定的充分条件;同时当系统是概周期系统时,通过构造适当的Liapunov函数,建立了相应系统存在唯一、全局渐近稳定的概周期正解的充分判据.     

具有脉冲和时滞的Logistic模型的持续生存和正周期解的全局吸引性(英文)

本文研究了具有脉冲和时滞效应的Logistic模型.利用脉冲微分方程的比较定理,BohlBrower不动点定理和Lyapunov函数法,获得了系统持续生存,正周期解存在、唯一以及全局吸引的充分条件.结果表明正周期解的全局吸引性与时滞有关.     

多频激励软弹簧型Duffing系统中的混沌

研究了多频激励下的软弹簧型Duffing系统的混沌动力学,发现混沌产生的根本原因是系统相空间中横截异宿环面的存在．建立了双频激励情况下二维环面上的Poincaré映射、稳定流形和不稳定流形,应用Melnikov方法给出了稳定流形和不稳定流形横截相交的条件,并将此方法推广到激励包含有限多个频率的情形．推广了Melnikov方法在高维系统中的应用,给出了Smale马蹄意义下混沌存在的判据．同时证明,激励频率数目的增加扩大了参数空间上的混沌区域．     

Global well-posedness of the hydrodynamic model for two-carrier plasmas

We prove results on the global well-posedness of the hydrodynamic model for two-carrier plasmas in whole space and periodic domain. We remove a technical condition which was first introduced by Alì and Jüngel [2] and developed in  and  to deal with the difficulty mainly arising from complicated coupling and cancellation between two carriers. The proofs depend on a result on continuity for compositions in Chemin–Lerner spaces and an elementary fact which indicates the connection between homogeneous and inhomogeneous Chemin–Lerner spaces.     

Existence of positive periodic solutions of an SEIR model with periodic coefficients

An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.     

具有反馈控制的N种群非自治LOTKA-VOLTERRA竞争系统的概周期解的存在性

讨论了具有反馈控制的N种群非自治LOTKA-VOLTERRA竞争系统,获得了该系统概周期解的存在性和全局稳定性,改进了概周期解研究的方法.     

具有多个时滞的周期Lotka-Volterra系统(英文)

1 IntroductionThe LotkaVOlterra system is a rudimentary model on mathematical ecologyand has been studied extensively; one can see that the two--species predator-prey nonautonomous LotkaVolterra system and the two-predator and one-prey periodic Lotka-VOlterra system have been investigated, respectively, in[21 and [31. Some sufficient conditions are obtained for the (unifOrm) persi-stence, existence and uniqueness, and asymptotic stability of periodic solu-tions. Furthermore, the similar re…     

A periodic predator–prey-chain system with impulsive perturbation

A periodic predator–prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied.