一类时滞三阶微分方程概周期解的存在性

运用二分性及压缩映射原理,研究一类时滞三阶微分方程概周期解的存在性,得到此类微分方程的概周期解存在的充分性定理．     

Positive almost periodic solutions for a delay logarithmic population model

By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.     

Stability of time-varying switched systems with time-varying delay

In this paper, we investigate the stability of time-varying switched systems with time-varying delay. We first give a generalization of Halanay’s inequality and then use this inequality to obtain sufficient conditions for the stability of switched systems.     

具有常数输入的非自治SIR流行病模型周期解的存在性

利用MAWHIN重合度理论中的延拓定理研究了一类具有常数输入的非自治SIR流行病模型的非平凡周期解的存在性.并用MatLab对其进行了数值模拟,作出了模型的相图和解曲线图形.     

The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems

This paper is concerned with a class of Nicholson blowfly systems with multiple time-varying delays. By applying the method of the Lyapunov functional, some criteria are established for the existence and uniqueness of positive periodic solutions of the system. Moreover, an example is given to illustrate the main results.     

An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using analytic methods, inequality technique and M-matrix theory, several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution are derived. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. Some existing results are improved and extended. The obtained results are less restrictive than previously known criteria, and the hypothesis for the boundedness and monotonicity on the activation functions and the differentiability on the time-varying delays are removed. An example is given to show the effectiveness of the obtained results.     

On the existence of periodic solutions to p-Laplacian Rayleigh differential equation with a delay

In this paper, the authors study the existence of periodic solutions to a p-Laplacian Rayleigh differential equation with a delay as follows:

(φp(y^′(t))^)′+f(y^′(t))+g(y(t−τ(t)))=e(t),     

STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot…     

Global existence of periodic solutions in an infection model

In this paper, a HTLV-I infection model with CTL immune response is considered. Taking the immune delay as a bifurcation parameter we investigate the global existence of periodic solutions of this model which shows existence of multiple periodic solutions theoretically.     

Existence of positive periodic solutions for a nonautonomous neutral delay n-species competitive model with impulses

In this paper, by using some analysis techniques and a new existence theorem, which is different from Gaines and Mawhin’s continuation theorem and abstract continuation theory for k-set contraction, we obtain some sufficient and realistic conditions for the existence of positive periodic solution of a general neutral delay n-species competitive model with impulses. As an application, we also examine some special cases which have been studied extensively in the literature. Some known results are improved and generalized.     

New results of existence and stability of periodic solution for a delay multispecies Logarithmic population model

In this Letter, for a general class of delayed periodic multispecies Logarithmic population model, we prove some new results on the existence of positive periodic solutions by contraction principle. The global exponential stability of positive periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.     

Stability analysis for stochastic jump systems with time-varying delay

This paper deals with the mean-square asymptotic stability of stochastic Markovian jump systems with time-varying delay. Based on a new stochastic inequality and convex analysis property, some novel stability conditions are presented. In the derivation, the information of the time-varying delay is retained and the estimation of it by the worst-case enlargement is not involved. Some special cases of the systems under consideration are also investigated. Illustrative examples are given to show the effectiveness of the proposed approach.     

Global existence of periodic solutions on a simplified BAM neural network model with delays

A simplified n-dimensional BAM neural network model with delays is considered. Some results of Hopf bifurcations occurring at the zero equilibrium as the delay increases are exhibited. Global existence of periodic solutions are established using a global Hopf bifurcation result of Wu [Wu J. Symmetric functional-differential equations and neural networks with memory. Trans Am Math Soc 1998;350:4799–838], and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney [Li MY, Muldowney J. On Bendixson’s criterion. J Differ Equations 1994;106:27–39]. Finally, computer simulations are performed to illustrate the analytical results found.     

Global existence of periodic solutions in a special neural network model with two delays

A simple neural network model with two delays is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when the sum of two delays passes through a sequence of critical values. Using a global Hopf bifurcation theorem for FDE due to Wu [Wu J. Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 1998;350:4799–838], a group of sufficient conditions for this model to have multiple periodic solutions are obtained when the sum of delays is sufficiently large. Numerical simulations are presented to support the obtained theoretical results.     

一类基于比率的且具有收获率和时滞的捕食系统的周期解

研究一类基于比率且具有收获和时滞的捕食系统．证明了系统正周期解的存在性,并通过构造适当的Lyapunov泛函,给出了正周期解全局稳定的充分条件．