一类生物捕食系统的定性分析

对一类两种群均有收获率的具较为特殊的功能反应函数的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,此类生物捕食系统平衡点的性态和极限环的存在,不存在及唯一的条件,获得了一类食饵-捕食系统的定性分析结果.     

一类捕食与被捕食模型极限环的存在性

本文考虑一类被捕食种群为线性密度制约，捕食者种群无密度制约且具ＨｏｌｌｉｎｇⅠ型功能性反应的捕食与被捕食两种群模型　得到了系统存在极限环的必要条件，且证明了当ｂ充分小时，系统至少存在两个极限环。     

具有HOLLINGⅢ型功能性反应的两种群捕食—被捕食系统的极限环和中心的存在性

本文通过对研究具有HOLLINGⅢ型功能性反应的两种群捕食－被捕食系统,得到其极限环和中心存在性的充分条件,并得到中心的个数以及相应的条件。     

一类具有线性收获率的生物捕食系统的定性分析

对一类两种群均有线性收获率的具HollingII类功能反应的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,得到此类生物捕食系统的平衡点的性态和极限环的存在,不存在的条件,从而对更具一般性的一类具有非常数收获率的食饵-捕食系统作了较为全面的定性分析,补充完善了前人的结果.     

具扩散与年龄结构的三种群捕食与被捕食系统的最优收获

研究了一类具有空间扩散和年龄结构的三种群捕食与被捕食系统的最优收获问题,运用Banach不动点原理讨论了系统解的存在唯一性,证明了最优收获控制的存在性,给出了最大值原理.结果可为多种群扩散系统最优控制问题的实际研究提供理论基础.     

环境污染中具有脉冲效应的捕食系统动力学分析

针对环境问题日益严峻,考虑到种群密度制约项的影响,建立了环境污染中脉冲输入污染物,且具有HollingⅡ型的两种群捕食与被捕食系统的动力学模型.利用脉冲微分方程的积分均值法和比较定理,得到系统弱平均持续生存和种群灭绝的充分条件.理论可用来保护物种,尤其是濒临灭绝的物种,防止灭绝.     

一类食饵具有不育控制的捕食模型

讨论了一类食饵具有不育控制的两种群捕食模型,得到了系统平衡点的存在条件,证明了平衡点的局部渐近稳定性和全局稳定性,最后给出了全局稳定的数值模拟,以及对参数进行了分析讨论.     

具有食饵避难的Leslie-Gower捕食系统最优收获分析

研究了一类具有食饵避难的Leslie-Gower捕食与被捕食系统收获模型,利用Hurwitz判据,得到了正平衡点局部渐近稳定,进一步构造了适当的Lyapunov函数,证明了正平衡点的全局渐近稳定性.并且在捕获努力量假说下,对发生食饵避难的两种群同时捕获,考虑了生态经济平衡点的存在性和利用Pontryagin最大值原理对两种群进行最优收获,得到当贴现率为零时,既保持了生态平衡,又使得在渔业开发过程中取得最大经济利益.     

具有阶段结构和时滞的捕食系统

本文中 ,我们考虑具有阶段结构和两个时滞的两种群捕食系统 .对于时滞τ1+τ2 =0 ,我们得到了两个种群持续生存和一个种群或两个种群绝灭的充分必要条件 .当τ1+τ2 增加到正平衡点不稳定时 ,系统存在一个小振幅的周期解 .     

一类具有常数脉冲投放的三种群捕食系统

考虑了一类两食饵种群具有密度制约和常数脉冲投放的三种群捕食系统,证明了当无捕食者时系统存在一个正周期解,并讨论了这个正周期解的全局渐近稳定性及其条件.     

THE LIMIT CYCLE OF A CLASS OF DYNAMICAL SYSTEM ABOUT CHEMICAL REACTION

1IntroductionInachemicalreaction'A-Al,itcanbeseenthatreactionspeedisapproximatelydirectratiototheconcentrationofreactant.Butreactionspeedisnotinfinitelyincreasingastheincreasingofconcentrationofreactant,thatis,ithasasaturatedreactionspeed.Oneoftherelation…     

Qualitative stability of certain nonlinear systems

To certain nonlinear dynamical systems naturally correspond simplicial complexes. This correspondence is a generalization of the familiar relationship between the interaction matrix of a linear dynamical system and the signed digraph of that matrix. By defining stability in terms of attractor regions (as opposed to attractor trajectories), we can specify qualitative linear algebraic conditions involving the simplicial complex which insure stability of the nonlinear system. The analysis uses only signs of coefficients in the dynamical system. A model of E. Lorenz [3] is an example of a three-dimensional system which fulfills the stability conditions and which is known to have a strange attractor within the attractor region. In summary, the linear qualitative tests described (Theorems 2 and 3) can be applied to certain nonlinear dynamical systems to yield preliminary information about the global stability of such systems.     

一个相互干扰的食植系统的定性分析

本文运用微分方程定性理论讨论了一个相互干扰的食植系统(2),获得了该系统在J(r_2+η1/Kδ~(1/2)) <1时,极限环存在唯一以及在J(r_2+η1/Kδ~(1/2)≥1时;正平衡点全局渐近稳定。     

生化反应中一类动力系统的定性分析

继续和完善了文[1-3]的工作,利用常微分方程定性理论,研究了生化反应中的一类动力系统dx并获得了该系统极限环的存在性,不存在性及极限环的存在惟一性的完整结果.     

A singular perturbation approach for a reaction diffusion system arising in nuclear reactor theory

The qualitative behavior of the solutions of a reaction-diffusion system arising in the theory of nuclear reactors is investigated by means of singular perturbation techniques, the small parameter ? representing the inverse of neutron velocity. At the lowest approximation for small ? the solutions exhibit oscillations about the unique strictly positive equilibrium, much as in the case of the associated lumped parameter system. A two-times representation for solutions of small amplitudes is also given.     

Qualitative and quantitative combined nonlinear dynamics model and its application in analysis of price,supply–demand ratio and selling rate

The qualitative and quantitative combined nonlinear dynamics model proposed in this paper fill the gap in nonlinear dynamics model in terms of qualitative and quantitative combined methods, allowing the qualitative model and quantitative model to perfectly combine and overcome their weaknesses by learning from each other. These two types of models use their strengths to make up for the other’s deficiencies. The qualitative and quantitative combined models can surmount the weakness that the qualitative model cannot be applied and verified in a quantitative manner, and the high costs and long time of multiple construction as well as verification of the quantitative model. The combined model is more practical and efficient, which is of great significance for nonlinear dynamics. The qualitative and quantitative combined modeling and model analytical method raised in this paper is not only applied to nonlinear dynamics, but can be adopted and drawn on in the modeling and model analysis of other fields. Additionally, the analytical method of qualitative and quantitative combined nonlinear dynamics model proposed in this paper can satisfactorily resolve the problems with the price system’s existing nonlinear dynamics model analytical method. The three-dimensional dynamics model of price, supply–demand ratio and selling rate established in this paper make estimates about the best commodity prices using the model results, thereby providing a theoretical basis for the government’s macro-control of price. Meanwhile, this model also offer theoretical guidance to how to enhance people’s purchasing power and consumption levels through price regulation and hence to improve people’s living standards.     

Hopf bifurcation and analysis of equilibrium for a third-order differential equation in a model of competition

1. IntroductionOne of the more challenging aspects of mathematical biology is competition modelling.Although the mathematical idea is simple[1], this type of modelling is so difficult to carryout in any generality since there are so maily ways for a population to compete.The simplest form of competition is called eXPloitative competition. This occurs whenone or more populations compete for the same resources such as a common food supplyor a growth-limiting nutriellt. A simple example of this…     

Synthetic Wisdom: The Design of a Mixed-Mode Modelling System for Organizational Decision Making

This paper discusses some of the early thinking about the development of a conference-based decision support system. It presents a scheme for the practical development of the mapping of argumentation (‘cognitive mapping’), particularly in the field of strategic planning. The objective is to redesign software (COPE) so that it may become both an effective conferencing system for the collection of ‘synthetic wisdom’ and yet also facilitate the analysis of the qualitative and quantitative features of the models so constructed. It stresses the need for the system to be able to cope with both the political and the behavioural aspects of the decision-making arena.     

基于云模型的定性运算理论与方法

将定性值像定量值一样参与运算和推导,是定性理论走向真正实际应用必须解决的极为关键的研究问题.相关研究提出的方法在此方面均有一定的局限性.本文提出了一种基于云模型的定性运算理论与方法.首先在云模型基本运算的基础上提出了基于云模型的定性关系演算方法,其次提出了基于云模型的一元一次定性方程的求解方法.理论和方法能比较科学合理地计算出定性值,且具有定性与定量相互融合的特点.为定性演算和推导在系统分析和仿真等领域中进一步应用提供了重要的借鉴方法.     

基于α—水平截集的模糊TOPSIS方法在公共危机管理能力评价中的应用研究

科学、客观地评价公共危机管理能力,对于完善危机管理系统有着重要的意义。本文从危机前预警能力,危机中处理能力和危机后恢复能力三个维度构建了公共危机管理能力评价指标体系。考虑到人们对复杂事物判断的模糊性,采用三角模糊数将专家给出的定性评价结果量化,结合α-水平截集和TOPSIS建立了公共危机管理能力综合评价模型,并通过求解非线性规划问题得出危机管理能力的模糊相对贴近度,进而去模糊化得出评价结果。最后用该模型对公共危机管理能力进行实证分析,验证了该模型的可行性和有效性。