随机变时滞不确定性系统的鲁棒稳定性

本文讨论了一类随机变时滞不确定性线性微分系统的鲁棒稳定性。参数的不确定性表现为参数是随时间变化的未知函数,但是时范数有界的。利用线性矩阵不等式和Lyapunov函数的方法给出一些相关的稳定性结论。     

Convergence of one-leg methods for nonlinear neutral delay integro-differential equations

Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper. This work was supported by National Natural Science Foundation of China (Grant No. 10871164), the Natural Science Foundation of Hunan Province (Grant No. 08JJ6002), and the Scientific Research Fund of Changsha University of Science and Technology (Grant No. 1004259)     

Stability and Hopf bifurcation for a regulated logistic growth model with discrete and distributed delays

In this paper, we investigate the stability and Hopf bifurcation of a new regulated logistic growth with discrete and distributed delays. By choosing the discrete delay τ as a bifurcation parameter, we prove that the system is locally asymptotically stable in a range of the delay and Hopf bifurcation occurs as τ crosses a critical value. Furthermore, explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by normal form theorem and center manifold argument. Finally, an illustrative example is also given to support the theoretical results.     

关于Triebei空间上的算子值傅里叶乘子

利用Stroemberg-Torchinsky分解,给出了Triebel空间Fp-q（R^n,X）上算子值傅里叶乘子的一个充分条件．在n〈min（p,q）情形下,这里给出的充分条件改进了之前已知的结果．     

一类具有时滞的比率依赖型捕食者-食饵系统周期正解的存在性

考虑一类具有时滞的比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理,得到系统存在正周期解的充分条件.     

Razumikhin-type theorems on exponential stability of impulsive delay systems

^** Corresponding author. Email: xzliu{at}math.uwaterloo.ca This paper studies the exponential stability of impulsive delaysystems. By employing the Razumikhin technique and Lyapunovfunctions, several exponential stability criteria are establishedfor both linear and non-linear impulsive delay systems. Someexamples are also worked through to illustrate our results.     

Influence of noise and delay on reaction-diffusion recurrent neural networks

In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks （RNNs） with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.     

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u≡1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain.     

Remarks on the paper [Appl. Math. Comput. 207 (2009) 388-396]

In this paper, some sufficient conditions are established for the oscillation of second-order neutral differential equations

     

Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay

We deal in this paper with the mild solution for fractional semilinear differential equations with infinite delay: with T>0 and 0<α<1. We prove the existence (and uniqueness) of solutions, assuming that A generates an α-resolvent family (S_α(t))_t?0 on a complex Banach space X by means of classical fixed points methods.