一类含有无限时滞和离散时滞的Logistic系统的全局渐近稳定性

考虑了一类含有无限时滞和离散时滞的非自治Logistic系统。通过运用时滞泛函微分方程的基本原理及新的计算技巧表明系统是持久的,且系统在持久性条件下也是全局渐近稳定的。结果表明时滞是“有害的”,获得了一些新的结果并改进了一些已有的结果。     

一类时滞非自治Lotka-Volterra竞争系统的灭绝性

讨论一类具有离散时滞和连续分布时滞的Lotka-Volterra系统,通过构造Lyapunov函数并引入上下平均的概念,将[3]和[6]的方法结合在一起,得到比[6]种群灭绝条件弱的充分条件,同时把文献[3]的结果推广到了时滞非自治系统上.     

扩散与时滞有关的单种群植物模型的全局稳定性

研究了具有周期系数及扩散与时滞有关的单种群植物模型,得到了该系统存在全局渐近稳定的正周期解的充分条件,其中该条件依赖时滞与扩散     

一个时滞微分系统的稳定性与Hopf分支

给出了一个三维时滞微分系统的平衡点的全时滞稳定的代数判据。也讨论并给出了这个系统存在Hopf分支的条件,两个例子说明了本文定理的应用。     

具变时滞细胞神经网络系统解的稳定性与Hopf分岔（英文）

在本文中,我们利用不动点理论和技巧,结合一类变时滞细胞神经网络系统的动力特征,研究其概周期解的存在性,在传递函数去掉有界的条件下,得到其不依赖于时滞的解的存在唯一性。进一步应用指数D-划分法,讨论系统的平衡点的性态,给出其稳定性和Hopf分岔存在的充分条件.再者我们研究具有时滞随机细胞神经网络系统解的指数稳定性,得到了当该系统的扰动项满足Lipschitz条件时的一些几乎必然指数稳定性的代数准则.     

KOLMOGOROV模型的无害时滞

1．引言考虑具有时滞的两种群相互作用模型的稳定性。其中τ_ij∈〔0,∞）,i,j=1,2．f和g对所含变元连续。假设存在正常数平衡点（x~*,y~*）,x~*＞0,y`*＞0,使得f（x~*,y~*)=g（x~*,y~*）＝0．系统（1）的特别情形是（1）中当τ_ij=0时得到著名的Kolmogorov模型。定义⑴系统（1"'）具有一类型的时滞,如果个时滞无论大小如何都不改变系统（1"）的平衡位置（x~*,y`*）的渐近稳定性,则称此时滞为无害时滞。文献〔1〕-〔3〕得到系统（1'）类型的时滞为无害时滞的充分条件。文献〔2〕提出这样一个有趣的问题：系统（1）类型的时滞…     

一种广义马尔科夫跳变时滞系统的保成本控制

针对广义马尔科夫跳变时滞系统,考虑了保成本控制问题.基于线性矩阵不等式的方法,给出了广义马尔科夫跳变时滞系统在模态独立条件下保成本控制器存在的充分条件.在所得结果基础上,进一步以线性矩阵不等式形式,给出了模态独立控制器增益的求解方法,实现了对广义马尔科夫跳变时滞系统的保成本控制.最后,通过数值例子验证了本文设计方法的有效性.     

具有时滞和反馈控制的Logistic增长模型的正周期解

首次研究同时具有状态依赖时滞和连续时滞的反馈控制Logistic增长模型,利用重合度理论研究其正周期解的存在性问题,得到了该系统周期正解存在的充分性条件,同时通过构造适当地Lyapunov泛函得到保证该系统（在适当限制下）存在全局稳定周期解的充分性条件,得到一些新结果,所得结果推广和改进了相关文献的主要结果。     

具有时滞的一捕食者-两食饵比率型生态系统的持久性与稳定性

研究一个具有时滞的一捕食者－两食饵比率型生态系统,证明了该系统在适当条件下的一致持久性。通过构造Lyapunov泛函,得到了该系统正平衡点局部渐近稳定的充分条件。     

具有三个年龄阶段的单种群自食模型

建立并研究了两个具有三个年龄阶段的单种群自食模型．这篇文章的主要目的是研究时滞对种群生长的作用,对于没有时滞的的模型,我们利用Liapunov函数,得到了系统平衡点全局渐近稳定的充分条件;而具有时滞的的模型,我们得到,随着时滞T增加,当系数满足一定条件时,正平衡点的稳定性可以改变有限次,最后变成不稳定;否则,时滞模型的正平衡点的稳定性不改变。     

Duration time of a one-dimensional random walk as a function of the energies of the intermediate states: application for dissociation and relaxation processes in DNA hybrids.

Kinetic parameters of macromolecular systems are important for their function in vitro and in vivo. These parameters describe how fast the system dissociates (the characteristic dissociation time), and how fast the system reaches equilibrium (characteristic relaxation time). For many macromolecular systems, the transitions within the systems are described as a random walk through a number of states with various free energies. The rate of transition between two given states within the system is characterized by the average time which passes between starting the movement from one state, and reaching the other state. This time is referred to as the mean first-passage time between two given states. The characteristic dissociation and relaxation times of the system depend on the first-passages times between the states within the system. Here, for a one-dimensional random walk we derived an equation, which connects the mean first-passage time between two states with the free energies of the states within the system. We also derived the general equation, which is not restricted to one-dimensional systems, connecting the relaxation time of the system with the first-passage times between states. The application of these equations to DNA branch migration, DNA structural transitions and other processes is discussed.     

Variables Aggregation in Time Varying Discrete Systems

In this work we extend approximate aggregation methods in time discrete linear models to the case of time varying environments. Approximate aggregation consists in describing some features of the dynamics of a general system involving many coupled variables in terms of the dynamics of a reduced system with a few number of variables. We present a time discrete time varying model in which we distinguish two time scales. By using perturbation methods we transform the system to make the global variables appear and build up the aggregated system. The asymptotic relationships between the general and aggregated systems are explored in the cases of a cyclically varying environment and a changing environment in process of stabilization. We show that under quite general conditions the knowledge of the behavior of the aggregated system characterizes that of the general system. The general method is also applied to aggregate a multiregional time dependent Leslie model showing that the aggregated model has demographic rates depending on the equilibrium proportions of individuals in the different patches.     

The Evolution of the Linnaean Hierarchy

The Linnaean system of classification is a threefold system of theoretical assumptions, sorting rules, and rules of nomenclature. Over time, that system has lost its theoretical assumptions as well as its sorting rules. Cladistic revisions have left it less and less Linnaean. And what remains of the system is flawed on pragmatic grounds. Taking all of this into account, it is time to consider alternative systems of classification.     

Variability in a single compartment system: A note on S. R. Bernard's model

In this note we examine a continuous time version of a compartmental model introduced in a discrete time setting by S. R. Bernard. The model allows for more than one particle to leave the system at any time. This introduces additional randomness into the system, over the pure death system and this is reflected in the variance function.     

Return time and vulnerability for a food chain model

Simulation studies have shown that the time it takes for a system of interacting species in a food chain to return to equilibrium after a disturbance increases as the number of trophic levels increase. It has been argued that this effect is important in limiting the length of food chains subject to perturbations of the real world. We show that for an asymptotically stable system a lower bound on the return time is directly proportional to the number of trophic levels in agreement with simulation studies. In addition, the lower bound on the return time is shown to be inversely proportional to the sum of products of the intraspecific competition coefficient and equilibrium population of the species. A new method for directly computing the vulnerability of a system to external perturbations is presented. Using this method we demonstrate that for a food chain where the number of species is equal to the number of trophic levels, the return time alone is not a proper measure of system vulnerability. Indeed, adding an additional trophic level may make the system less vulnerable to disturbances. Interspecific coupling between the trophic levels is shown to be an important factor in determining system vulnerability.     

Integrative biology: linking levels of organization

Biological systems are composed of different levels of organization. Usually, one considers the atomic, molecular, cellular, individual, population, community and ecosystem levels. These levels of organization also correspond to different levels of observation of the system, from microscopic to macroscopic, i.e., to different time and space scales. The more microscopic the level is, the faster the time scale and the smaller the space scale are. The dynamics of the complete system is the result of the coupled dynamical processes that take place in each of its levels of organization at different time scales. Variables aggregation methods take advantage of these different time scales to reduce the dimension of mathematical models such as a system of ordinary differential equations. We are going to study the dynamics of a system which is hierarchically organized in the sense that it is composed of groups of elements that can be themselves divided into further smaller sub-groups and so on. The hierarchical structure of the system results from the fact that the intra-group interactions are assumed to be larger than inter-group ones. We present aggregation methods that allow one to build a reduced model that governs a few global variables at the slow time scale.     

Characterization of the transit and transition times for a pathway unit of Michaelis-Menten mechanism

The transit time and a characteristic time constant for the transition time are formulated for a pathway unit of Michaelis-Menten mechanism in metabolic chains with mass-action-type dependence. The pathway unit in a chain is assigned to each metabolite and two consecutive Michaelis-Menten-type reactions associated with it. All the relevant functions such as control coefficients, elasticities and transit time for the pathway unit are expressed in terms of the flux J and other system parameters. The transition time is characterized by a time constant for a first-order system expressed as the derivative of the total concentration of the internal metabolite with respect to the flux J.     

Aging and the metrics of time

In contrast to clock time, which is extrinsic, universal and reversible, age is an intrinsic, directed measure of the state of a particular system. It is proposed that if the dynamical equations of a given system are cast into canonical form, a time scale intrinsic to that system can be derived. The metric which converts a given intrinsic time to clock time is derived in terms of the given system's constitutive parameters. Age becomes a question of similitude, two systems being in corresponding states (i.e. at the same age) at identical instants of intrinsic time (not clock time).It is further proposed that there is an intrinsic time associated with any dissipative process and that the coupling coefficients, L_ik, of irreversible thermodynamics are metrics which scale the passage of intrinsic time to clock time as measured by a standard harmonic oscillator. Thus in addition to the long standing conjecture that entropy production determines the direction of time's arrow there also is a sense in which it determines the rate of its flow.     

Application of the transition time of metabolic system as a criterion for optimization of metabolic processes

Transition time of metabolic systems in introduced as a suitable optimization criterion for biotechnological processes in which it is desirable to reduce the lag time and minimize the mass contained within the system. Lag time is the time needed for the system to attain the steady state. Results obtained from the sensitivity analysis of this steady state response are presented within the metabolic control analysis and applied to 3 case studies. In all of them the information provided by the transition time control profile allows the implementation of a strategy for biotechnological manipulations aimed at the improvement of the process. (c) 1994 John Wiley & Sons, Inc.     

Fitz-Hugh Nagumo系统的渐近稳定性

用无穷维动力系统的方法研究了Fitz-Hugh Nagumo神经系统中沿神经细胞轴突信号传递的长时间行为.在齐次边界条件与非齐次边界条件下证明了系统在其不变流形上的全局吸引子为系统在该不变流形内的唯一平衡点,从而证明了该系统的渐近稳定性.