变时滞区间细胞神经网络的全局鲁棒稳定性

利用拓扑度理论和Liapunov泛函方法讨论了变时滞区间细胞神经网络的全局鲁棒稳定性．给出了实用有效的判定条件,推广了有关文献中的结果．     

一类具反应扩散项的时滞耦合神经网络的同步

主要讨论一类具有反应扩散项混合时滞耦合神经网络的同步问题.同时,考虑系统参数的范数有界不确定性及其切换依赖某个马尔可夫链等方面对其的影响.文中通过构造新颖的Lyapunov-Krasovskii泛函,运用线性矩阵不等式(LMI)技术并结合Kronecker积来获得耦合神经网络的鲁棒均方全局指数同步的充分性条件,并且所获得的判据依赖于时滞.该条件可由MATLAB的LMI工具箱进行有效的验证.此外,细胞激活函数更为一般的假设,可进一步减少结论的保守性.     

工业微生物遗传和环境扰动的调控和适应进化

开发工业微生物,使其利用可再生的原料生产生物燃料、大宗化学品、食品添加剂和营养品、药物以及工业酶等,是发展生物产业的基础。工业微生物高产和胁迫抗性等鲁棒性状受复杂遗传调控网络控制,其改造需要从全基因组尺度进行系统的全局的多位点的扰动,以达到快速积累多样性基因型突变并产生所期望的表型。文中对工业微生物鲁棒性状的遗传调控与胁迫响应机制、基因组全局扰动与多位点快速进化以及细胞水平氧还平衡的全局扰动进行了简要综述,未来需要继续借助系统生物学和合成生物学手段,进一步加强对工业环境下工业微生物鲁棒性状调控机理的解析与建模预测以及系统的工程改造。     

带脉冲的BAM神经网络的全局指数稳定性

利用M矩阵理论,推广的微分不等式和Lyapunov函数,研究了一类带时滞和脉冲的BAM神经网络平衡点的存在唯一性和全局指数稳定性条件.文中推广了以往文献脉冲函数的形式,无需时滞的可导性要求,从而减弱了以往结论的条件,并且可以估计网络的指数收敛速率.     

半定规划鲁棒不可行性研究

本文给出了一种判别半定规划鲁棒不可行的准则,通过该准则我们可判断模型对输入数据是否敏感,进而决定是否应该利用鲁棒优化建模的方法对模型进行重新建模,使其所求解具有鲁棒性.避免了所给模型在实际应用中存在较大的风险性,为更好的应用鲁棒优化建模方法提供了理论依据.     

变系数变时滞BAM神经网络概周期解的存在性与全局吸引性

利用指数二分性、Banach不动点定理与微分不等式分析技巧,在不要求激活函数有界的条件下,给出了变系数变时滞的BAM神经网络概周期解的存在唯一性和全局吸引性的充分条件．所得结果推广和改进了相应文献的结果。对设计BAM神经网络概周期振荡有重要意义．     

一类中立型Hopfield神经网络的全局吸引集

讨论了中立型Hopfield神经网络模型,利用矩阵谱的性质和微分不等式分析等技巧,给出了其不变集和全局吸引集的判别准则．特别地,当系统有平衡点时,我们也得到了平衡点全局稳定的判别条件．     

一类Hopfield型时滞神经网络模型的全局渐近稳定性

用拓扑度和Lyapunov泛函方法，讨论了一类具有时滞的Hopfield神经网络平衡点的存在性及其全局渐近稳定性．所获得的若干判别条件，都去掉了有关文献中关于激活函数的可微性和有界性限制，增强了模型的适用性．     

具有免疫反应和细胞内时滞的病毒动态模型（英文）

本文研究了一类具有免疫反应和细胞内时滞的病毒动态学模型.通过构造李雅普诺夫函数和应用Lasalle不变原理,得到:模型的全局动力学行为是完全由基本的再生数决定的,并在一定条件下,无病平衡点和地方病平衡点是全局稳定的.我们的结果可以应用到许多发生率函数,如线性发生率函数、标准发生率函数,等等.最后,我们做了数值模拟来验证我们的理论分析并提出了控制病毒感染的方法.     

具有时滞的细胞神经网络模型的全局指数稳定性

利用拓扑度理论、推广的Halanaly矩阵时滞微分不等式、Lyapunov原理以及Dini导数,研究了具有时滞的细胞神经网络模型的全局指数稳定性．去掉了有关文献中要求输出函数fj在实数集R上有界、可微的条件,给出了更弱的判定平衡点的存在唯一性以及全局指数稳定性的判据,推广和改进了前人的相关结论,最后的数值例子说明本文结果不仅保守性小,而且计算简单．     

Robust stability of genetic regulatory networks with distributed delay

This paper investigates robust stability of genetic regulatory networks with distributed delay. Different from other papers, distributed delay is induced. It says that the concentration of macromolecule depends on an integral of the regulatory function of over a specified range of previous time, which is more realistic. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for genetic regulatory networks to be global asymptotic stability and robust stability are derived in terms of LMI. Two numerical examples are given to illustrate the effectiveness of our theoretical results.     

Global robust power-rate stability of delayed genetic regulatory networks with noise perturbations

In this paper, by using the Lyapunov method, Itô’s differential formula and linear matrix inequality (LMI) approach, the global robust power-rate stability in mean square is discussed for genetic regulatory networks with unbounded time-varying delay, noise perturbations and parameter uncertainties. Sufficient conditions are given to ensure the robust power-rate stability (in mean square) of the genetic regulatory networks. Meanwhile, the criteria ensuring global power-rate stability in mean square are a byproduct of the criteria guaranteeing global robust power-rate stability in mean square. The obtained conditions are derived in terms of linear matrix inequalities (LMIs) which are easy to be verified via the LMI toolbox. An illustrative example is given to show the effectiveness of the obtained result.     

The range of time delay and the global stability of the equilibrium for an IVGTT model

Diabetes mellitus has become a prevalent disease in the world. Diagnostic protocol for the onset of diabetes mellitus is the initial step in the treatments. The intravenous glucose tolerance test (IVGTT) has been considered as the most accurate method to determine the insulin sensitivity and glucose effectiveness. It is well known that there exists a time delay in insulin secretion stimulated by the elevated glucose concentration level. However, the range of the length of the delay in the existing IVGTT models are not fully discussed and thus in many cases the time delay may be assigned to a value out of its reasonable range. In addition, several attempts had been made to determine when the unique equilibrium point is globally asymptotically stable. However, all these conditions are delay-independent. In this paper, we discuss the range of the time delay and provide easy-to-check delay-dependent conditions for the global asymptotic stability of the equilibrium point for a recent IVGTT model through Liapunov function approach. Estimates of the upper bound of the delay for global stability are given in corollaries. In addition, the numerical simulation in this paper is fully incorporated with functional initial conditions, which is natural and more appropriate in delay differential equation systems.     

一类随机时滞捕食者-食饵模型的动力学行为（英文）

研究了一类含时滞的Harrison型捕食者-食饵模型在随机扰动环境下的动力学行为.对于非时滞和时滞模型分别给出了局部和全局稳定性条件.通过白噪声分别对食饵人口增长率的和捕食者人口死亡率进行随机扰动,构建相应的随机时滞微分方程模型讨论环境噪声对其作用的动力学行为.在一定条件下,随机时滞模型存在随机最终有界的唯一全局正解且解的二阶均值是有界的.最后通过数值模拟对给出的分析结果进行了验证.     

The Impact of Time Delays on the Robustness of Biological Oscillators and the Effect of Bifurcations on the Inverse Problem

Differential equation models for biological oscillators are often not robust with respect to parameter variations. They are based on chemical reaction kinetics, and solutions typically converge to a fixed point. This behavior is in contrast to real biological oscillators, which work reliably under varying conditions. Moreover, it complicates network inference from time series data. This paper investigates differential equation models for biological oscillators from two perspectives. First, we investigate the effect of time delays on the robustness of these oscillator models. In particular, we provide sufficient conditions for a time delay to cause oscillations by destabilizing a fixed point in two-dimensional systems. Moreover, we show that the inclusion of a time delay also stabilizes oscillating behavior in this way in larger networks. The second part focuses on the inverse problem of estimating model parameters from time series data. Bifurcations are related to nonsmoothness and multiple local minima of the objective function.     

Global robust stability for shunting inhibitory CNNs with delays

In this paper, the problem of global robust stability for shunting inhibitory cellular neural networks (SICNNs) is studied. A sufficient condition guaranteeing the network's global robust stability is established. The result can easily be used to verify globally robust stable networks. An example is given to illustrate that the conditions of our results are feasible.     

具有边疆时滞和扩散的非自治Holling捕食系统的持续生存

本文给出了在具有连续时滞和Ⅱ类功能性反应及扩散的非自治捕食系统中，种群持续自下而上，周期解存在及全局渐近稳定的充分条件。     

一类含分布时滞的流行病模型的研究

提出了一类含分布时滞的流行病模型,利用构造李亚普诺夫泛函的方法,得到了无病平衡点和地方病平衡点全局稳定性的结论,揭示了平均时滞对各类平衡点稳定性的影响。     

Absolute stability in predator-prey models

An equilibrium of a time-lagged population model is said to be absolutely stable if it remains locally stable regardless of the length of the time delay, and it is argued that the criteria for absolute stability provide a valuable guide to the behavior of population models. For example, it is sometimes assumed that time delays have a limited impact until they exceed the natural time scale of a system; here it is stressed that under some conditions very short time delays can have a marked (and often maximal) destabilizing effect. Consequently it is important that our understanding of population dynamics is robust to the inclusion of the short time delays present in all biological systems. The absolute stability criteria are ideally suited for this role. Another important reason for using the criteria for absolute stability rather than using criteria which depend upon the details of a time delay is that biological time delays are unlikely to be constant. For example, a time delay due to maturation inevitably varies between individuals and the mean may itself vary over time. Here it is shown that the criteria for absolute stability are generally robust in the presence of distributed delays and of varying delays. The analysis presented is based upon a general predator-prey model and it is shown that absolute stability can be expected under a broad range of parameter values whenever the time delay is due to the maturation time of either the predator or the prey or of both. This stability occurs because of the interaction between delayed and undelayed dynamic features of the model. A time-delayed process, when viewed across all possible delays, always reduces stability and this effect occurs regardless of whether the process would act to stabilize or destabilize an undelayed system. Opposing the destabilization due to a time delay and making absolute stability a possibility are a number of processes which act without delay. Some of these processes can be identified as stabilizing from the analysis of undelayed models (for example, the type 3 functional response) but other cannot (for example, the nonreproductive numerical response of predators).