On the spectrum of almost periodic solution of second order scalar functional differential equations with piecewise constant argument

We study the spectrum containment of almost periodic solution to neutral delay differential equations with piecewise constant argument (EPCA, for short). We find an important property, which is different from that given by Cartwright for ordinary differential equations (ODE). Some known (periodic solution) results would be expanded. As a corollary, it is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. This new phenomenon is due to the piecewise constant argument and illustrates a crucial difference between ODE and EPCA.     

非线性退化时滞系统的周期解

本文利用不动点方法研究两类非线性退化时滞系统的周期解问题,获得了这两类 系统存在周期解的若干充分条件。     

非线性抛物型时滞微分方程解振动的充要条件

讨论了一类多滞量非线性抛物型时滞微分方程解的振动性质，获得了其一切解振动的充要条件；指出了其与普通抛物型偏微分方程解的质的差异。     

The optimal repair-time limit replacement policy with imperfect repair: Lorenz transform approach

In this paper, we consider a simple repair-time limit replacement problem with imperfect repair, and focus on the problem of determining the optimal repair-time limit which minimizes the expected cost per unit time in the steady-state. Applying the Lorenz transform, we develop a nonparametric method to estimate the optimal repair-time limit from the empirical repair-time data. Numerical examples are considered to calculate the optimal policy and to examine the asymptotic properties of the estimator.     

时滞Lotka-Volterra竞争型系统的概周期解

研究具有离散时滞的N-种群Lotka-Volterra竞争型系统，得到了系统存在唯一性概周期解的一组充分条件。     

非自治时滞微分方程正周期解的存在性

应用Krasnoselskii锥映射不动点定理，研究了具一般时滞非线性非自治Logistic方程的ω-周期解的存在性，获得了存在正周期解的充分条件．     

PERIODIC SOLUTION FOR DIFFUSIVE PREDATOR-PREY PATCH SYSTEMS WITH TIME DELAY AND PERIODIC STOCKING

In this paper, a three species difFusive predator-prey modei with functional response and periodic stocking is studied, where all parameters are time depen-dent. By using new theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.     

Mechanism Equivalence in Enzyme–Substrate Reactions: Distributed Differential Delay in Enzyme Kinetics

We consider single enzyme–substrate reaction mechanisms involving multiple complexes and demonstrate that these are equivalent to a distributed delay system without complexes. The distribution of the delay is determined by the number of intermediates and the relative sizes of the rates of the individual reaction mechanisms. We also consider the limit where there are a large number of intermediate complexes, and the conditions under which a number of known reaction mechanisms are equivalent. The present formalism brings forth new perspectives in the implementation of experimental techniques to rule out particular reaction mechanisms by studying the distribution of the delay between reactant mixing and product formation.     

Stability in the Numerical Solution of Linear Parabolic Equations with a Delay Term

This paper is concerned with the stability of numerical processes that arise after semi-discretization of linear parabolic equations wit a delay term. These numerical processes are obtained by applying step-by-step methods to the resulting systems of ordinary delay differential equations. Under the assumption that the semi-discretization matrix is normal we establish upper bounds for the growth of errors in the numerical processes under consideration, and thus arrive at conclusions about their stability. More detailed upper bounds are obtained for -methods under the additional assumption that the eigenvalues of the semi-discretization matrix are real and negative. In particular, we derive contractivity properties in this case. Contractivity properties are also obtained for the -methods applied to the one-dimensional test equation with real coefficients and a delay term. Numerical experiments confirming the derived contractivity properties for parabolic equations with a delay term are presented.     

Nonlinear Dynamical Behavior in Neuron Model Based on Small World Network with Attack and Repair Strategy

In this paper, we investigate the effect due to the change of topology structure of network on the nonlinear dynamical behavior, by virtue of the OFC neuron evolution model with attack and repair strategy based on the small world. In particular, roles of various parameters relating to the dynamical behavior are carefully studied and analyzed. In addition, the avalanche and EEC-like wave activities with attack and repair strategy are also explored in detail in this work.