一类半离散非线性时滞种群模型的稳定性

自然界的物种不是孤立存在的,考虑外来物种对种群的影响,增加一个额外的强迫力τ(t)是符合实际的.推导了一个带常数扰动项的半离散非线性时滞种群模型,研究了它的稳定性.研究结果显示,模型的零解为鞍点,而在某些参数条件下,模型的正平衡点具有局部渐进稳定性.     

一类非线性年龄等级结构种群模型的稳定性

该文分析一类基于年龄的等级结构种群模型正平衡态的存在性及零解的稳定性,在年轻个体占优的前提下用偏微分-积分方程描述种群演化进程.定义了种群再生数,运用非零不动点原理确立了该系统存在正平衡态,借助特征方程和Liapunov函数导出零解的局部和全局稳定结果,并做出数值验证.     

一类非线性年龄等级结构种群模型的数值解法

假设年轻个体在种群内部竞争中占优,建立一类非线性等级结构种群模型,它是具有全局耦合边界条件的偏微分-积分方程的初边值问题.提出该模型解的数值计算方法,证明算法的收敛性,并给出数值实验结果.     

一类非线性随机种群动力学模型的最优收获控制

研究了一类非线性随机种群动力学模型的最优收获控制问题,得出了在外界环境对系统产生影响的条件下,最优控制所满足的必要条件及其最优性组,所得到的结论是确定性种群系统的扩展.     

一类非线性年龄等级结构种群系统模型的可控性

研究一类基于年龄等级差异的种群系统的近似可控性问题,状态方程由非线性偏微分-积分方程描述,且边界条件具有全局反馈特征.运用冻结系数法、线性系统可控性和集值映射不动点原理确立了系统可控性,表明了种群状态可通过个体迁移调节.     

模拟弹性增长的非线性尺度结构种群模型分析

分析一类具有弹性增长的非线性尺度结构种群系统模型,个体生死率对密度制约的响应不同.运用耦合上下解方法、比较原理和延拓思想确立了模型非负有界解的存在唯一性;给出了正平衡态的存在性判据和表达式,导出了平衡态的特征方程,获得了稳定性判别准则,在不考虑死亡率的密度制约时还得到了正平衡态稳定性阈值.其结果为种群生存分析、状态逼近和控制问题研究奠定基础.     

一类非线性等级结构种群控制模型解的适定性

分析一类具有个体年龄等级差异的非线性种群系统模型解的适定性问题.运用特征线法、积分不等式和不动点原理证明了系统非负解的存在唯一性和有界性,以及解对控制变量的一致连续性.拓展了常见的年龄结构系统基本理论.为研究种群的长期演化和调控问题奠定基础.     

非线性种群增长方程的半群解

本文利用非线性半群的方法来讨论非线性种群增长方程,证明了非线性种群增长算子是Hilbert空间L~2(0,m)中的ω-单调算子并且是闭稠定的算子。它产生某个ω型非线性半群,而且非线性种群增长算子就是这个ω型非线性半群的无穷小母元,从而用非线性半群直接给出了种群增长方程解的存在唯一性。最后,我们将考虑带迁移项的种群增长方程解的存在唯一性。     

一类改进的非线性种群系统的最优控制

研究某一类改进的关于年龄结构的非线性种群系统的最优控制问题.首先利用常用的极小化序列方法证明最优控制问题的最优解存在;其次定义原系统对应的共轭系统,借助于法锥定义,得到最优解所要满足的必要条件.     

生物种群的一类统计模型

以往关于生物种群增长的数学模型多是用微分方程和概率极限定理的方法来推导的。本文改用回归分析 ,系数显著性检验和残差检验的方法 ,直接从统计数字出发 ,得出美国人口在1880— 1960年的人口数字增长模型——正态前升模型。它是拟合得很好的不同以往的模型。并给出了初步的解释。     

A CLASS OF VOLTERRA INTEGRAL EQUATIONS ARISING IN DELAYED-RECRUITMENT POPULATION MODELS

We formulate a Volterra integral equation which contains as special cases the differential-difference equation model of Blythe, Gurney and Nisbet for populations with delayed recruitment and a differential-difference equation with two delays related to the epidemic model of Wilson and Burke. We establish upper and lower bounds for positive solutions and give a classification of equilibria with conditions to determine whether an equilibrium is stable for all delays (absolutely stable), unstable for all delays, or switches from stable to unstable as the delay increases.     

NONLINEAR MATRIX MODELS AND POPULATION DYNAMICS

Nonlinear matrix difference equations are studied as models for the discrete time dynamics of a population whose individual members have been categorized into a finite number of classes. The equations are treated with sufficient generality so as to include virtually any type of structuring of the population (the sole constraint is that all newborns lie in the same class) and any types of nonlinearities which arise from the density dependence of fertility rates, survival rates and transition probabilities between classes. The existence and stability of equilibrium class distribution vectors are studied by means of bifurcation theory techniques using a single composite, biologically meaningful quantity as a bifurcation parameter, namely the inherent net reproductive rate r. It is shown that, just as in the case of linear matrix equations, a global continuum of positive equilibria exists which bifurcates as a function of r from the zero equilibrium state at and only at r = 1. Furthermore the zero equilibrium loses stability as r is increased through 1. Unlike the linear case however, for which the bifurcation is “vertical” (i.e., equilibria exist only for r = 1), the nonlinear equation in general has positive equilibria for an interval of r values. Methods for studying the geometry of the continuum based upon the density dependence of the net reproductive rate at equilibrium are developed. With regard to stability, it is shown that in general the positive equilibria near the bifurcation point are stable if the bifurcation is to the right and unstable if it is to the left. Some further results and conjectures concerning stability are also given. The methods are illustrated by several examples involving nonlinear models of various types taken from the literature.     

一类神经网络模型的稳定性

本文将一种求解凸规划问题的神经网络模型推广到求解一般的非凸非线性规划问题．理论分析表明;在适当的条件下,本文提出的求解非凸非线性规划问题的神经网络模型的平衡点是渐近稳定的,对应于非线性规划问题的局部最优解     

DYNAMICS IN A CLASS OF NEURON MODELS

In this paper, we investigate the dynamics in a class of discrete-time neuron mod-els. The neuron model we discussed, defined by such periodic input-output mapping as a sinusoidal function, has a remarkably larger memory capacity than the conven-tional association system with the monotonous function. Our results show that the orbit of the model takes a conventional bifurcation route, from stable equilibrium, to periodicity, even to chaotic region. And the theoretical analysis is verified by numerical simula...     

一类非线性粘弹方程

建立了一类粘弹方程全局解的存在性和相应的解半群.     

一类非线性算子的满射性

Hilbert空间中余弦值不为1的非线性算子构成了一类广泛的特殊的非线性算子.研究了这类非线性算子的满射性,并给出了其成立的几个充分条件.     

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied,in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions,and the structure of optimal control may be characterized.     

一类奇异型折扣费用模型之推广

设((?),(?),P)为一概率空间,(?)_t,t≥0为(?)中的上升(?)-域,W_t,t≥0为(?)_t,适应的标准 Wiener 过程,且对(?)0≤s≤t≤∞,W_t—W_s 与(?)_s 独立.以(?)表(?)_t 适应左连续0初值有限变差过程全体.对(?)ξ={ξ_t,t≥0}∈(?)有正规分解ξ_t=ξ_t~ —ξ_t~-,(?)_t(?)ξ_t~ ξ_t~-表ξ_t的全变差,当然ξ~ 及ξ_-皆(?)中单调非降过程.有关类型的折扣费用问题曾被不少人研究过,例如 Bene(?)等人的文章.后来这些     

ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR GENERALIZED SYSTEMS

§ 1　IntroductionAs compared with the ODEs system,the generalized system is of many distinctiveproperties[1 ] ,forexam ple,the level structural problem of system state solutions,the uncon-sistent initial value problem,the uniqueness of initial value problem and so on.The asymp-totic stability problem of zero solution of generalized system involves the tractability andunimpulsivity.These properties are of great importance in engineering applications.Theconclusion on the ODEs system can not …     

A CLASS OF MODELS FOR SKALA'S SET THEORY

For each ordinal α it is given a model for Skala's set theory using the well-known cumulative type hierarchy.