带有分布时滞带菌者的疾病模型行波解

对于带有分布时滞带菌者的疾病模型,当分布时滞核是—般的г分布时滞核时,通过线性链技巧和几何奇异扰动理论,本文证明带菌者的疾病模型行波解存在性.     

具有分布时滞的KdV方程的周期行波解的存在性

将研究具有分布时滞的K dV方程Ut+(f*U)Ux+τUxx+Uxxx=0,得出当时滞核函数为弱一般核时,时滞方程周期行波解的存在性.     

具有非局部反应的时滞扩散Nicholson方程的行波解

对具有扩散项的时滞Mcholson方程的行波解进行了研究.特别是考虑到生物个体在空间位置上的迁移,研究了具有非局部反应的时滞扩散模型.对于弱生成时滞核,运用几何奇异摄动理论,在时滞充分小的情况下,证明了行波解的存在性.     

一类含分布时滞革新传播模型的稳定性

本文建立了一类含分布时滞的革新传播模型，研究了分布时滞对传播过程的影响，讨论了正平衡点的存在性和唯一性以及正平衡点的渐近稳定性(全局和局部)，当分布时滞的核函数取形式ae^-at时，证明了正平衡点是绝对渐近稳定的。     

具有时滞和间接控制的捕食-被捕食模型的分支分析

研究了一类具有时滞和间接控制的捕食-被捕食模型.选择时滞τ为分支参数,证实了系统在一定的时滞范围内是渐近稳定的.当时滞τ通过一系列的临界值时,Hopf分支产生,即当时滞τ通过某些临界值时,从平衡点处产生一簇周期解.最后,用数值模拟验证了理论分析结果的正确性.     

带有记忆核的可拉伸时滞吊桥方程解的长时间行为（英文）

吊桥方程解的长期动力学行为已有许多经典结论,但关于时滞吊桥方程动力学行为的研究甚少.本文研究带有记忆核的可拉伸时滞吊桥方程解的长期动力学行为,利用压缩函数的方法,获得该时滞吊桥方程拉回吸引子的存在性.     

输入带有时滞的线性系统的镇定

考虑带有输入时滞的线性系统的镇定问题.通过把时滞写成一阶传播方程,带有输入时滞的镇定问题转化为常微分方程和一阶双曲方程组成的串联系统的镇定问题.与现有Backstepping方法不同,文章给出了新的变换,其核函数是一阶倒向向量值常微分方程,这使得控制的设计更加简单.文章给出了新的状态反馈控制器,并证明了闭环系统解的适定性和指数稳定性.数值模拟说明,给出的方法是非常有效的.     

一类具有时变时滞的中立型系统的稳定性分析

本文研究一类具有状态时滞和输入时滞的时变时滞线性中立型系统.首先,通过选取合适的Lya-punov-Krasovskii泛函,应用LMI方法和Lyapunov-Krasovskii稳定性定理对时滞相关的系统进行稳定性分析,并设计了相应的控制器.改进了时不变时滞线性系统方面的一些结果.最后用实例验证所得到结果.     

一类带有竞争和自反时滞的网站竞争系统的Hopf分支

不同于以往研究网站竞争系统时,仅考虑带有自反时滞或竞争时滞的情况,本文研究了一类同时带有竞争时滞和自反时滞的网站竞争系统,并以时滞作为分支参数,通过分析正平衡点处的特征方程,研究了正平衡点的稳定性,证明了Hopf分支的存在性,得到了发生Hopf分支时的临界的时滞值,最后通过数值模拟进一步验证了所得结论.     

多重时滞富营养化生态模型的稳定性与分支分析

本文研究了多重时滞富营养化生态模型的稳定性与分支问题.利用特征值方法,分别研究了具有单时滞和双时滞模型的线性稳定性.发现当模型中的时滞经过一系列临界值时,模型在平衡点附近经历了Hopf分支和Hopf-zero分支,并给出Hopf分支和Hopf-zero分支存在的充分条件.最后数值模拟验证了理论结果.     

Piecewise reproducing kernel method for singularly perturbed delay initial value problems

A direct application of the reproducing kernel method presented in the previous works cannot yield accurate approximate solutions for singularly perturbed delay differential equations. In this letter, we construct a new numerical method called piecewise reproducing kernel method for singularly perturbed delay initial value problems. Numerical results show that the present method does not share the drawback of standard reproducing kernel method and is an effective method for the considered singularly perturbed delay initial value problems.     

Traveling wave solutions for Schrödinger equation with distributed delay

The paper is devoted to study of traveling waves of nonlinear Schrödinger equation with distributed delay by applying geometric singular perturbation theory, differential manifold theory and the regular perturbation analysis for a Hamiltonian system. Under the assumptions that the distributed delay kernel is strong general delay kernel and the average delay is small, we first investigate the existence of solitary wave solutions by differential manifold theory. Then by utilizing the regular perturbation analysis for a Hamiltonian system, we explore the periodic traveling wave solutions.     

TRAVELING WAVES IN A BIOLOGICAL REACTION-DIFFUSION MODEL WITH STRONG GENERIC DELAY KERNEL AND NON-LOCAL EFFECT

In this paper,we consider the reaction diffusion equations with strong generic delay kernel and non-local effect,which models the microbial growth in a flow reactor.The existence of traveling waves is established for this model.More precisely,using the geometric singular perturbation theory,we show that traveling wave solutions exist provided that the delay is sufficiently small with the strong generic delay kernel.     

Travelling waves of the diffusive Nicholson’s blowflies equation with strong generic delay kernel and non-local effect

In this paper, we consider travelling wave solutions for the diffusive Nicholson’s blowflies equation incorporating time delay and diffusion. Special attention is paid to the modelling of the time delay to incorporate associated non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times. For the strong generic delay kernel, we show that travelling wave solutions exist provided that the delay is sufficiently small, using the geometric singular perturbation theory.     

Simplified reproducing kernel method for fractional differential equations with delay

This paper is devoted to the numerical scheme for the delay initial value problems of a fractional order. The main idea of this method is to establish a novel reproducing kernel space that satisfies the initial conditions. Based on the properties of the new reproducing kernel space, the simplified reproducing kernel method (SRKM for short) is applied to obtain accurate approximation. The Schmidt orthogoralization process which requires a large number of calculation is less likely to be employed. Numerical experiments are provided to illustrate the performance of the method.     

具有非局部反应的时滞扩散Nicholson方程的行波解

对具有扩散项的时滞Nicholson方程的行波解进行了研究．特别是考虑到生物个体在空间位置上的迁移,研究了具有非局部反应的时滞扩散模型．对于弱生成时滞核,运用几何奇异摄动理论,在时滞充分小的情况下,证明了行波解的存在性．     

Stability switch and Hopf bifurcation for a diffusive prey-predator system with delay

The increasing time delay usually destabilizes any dynamical system. In this paper we give an example that in some special cases the opposite effect can be experienced if the time delay is sufficiently great. We investigate the effect of both the parameter in the time delay kernel and diffusion coefficient on the stability of the positive steady state for a diffusive prey-predator system with delay. We obtain the condition of the occurrence of the stability switches of the positive steady state.     

A SPECTRAL METHOD FOR A WEAKLY SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATION WITH PANTOGRAPH DELAY

In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval [-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equat...