变时滞SIS流行病模型的稳定性分析

研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。     

具有扩散的n-斑块单种群系统的全局稳定性

研究了具有扩散的ｎ－斑块多种环境下单种群非自治模型,在假定该模型所有系数连续有界的情况下,得到了系统全局稳定的充分条件。     

具有庇护所的三种群捕食者-食饵模型

讨论了一类具有庇护所的自治三种群捕食者一食饵模型,运用Liapunov函数方法,得到了该模型持久性的充分条件．对于该模型的周期系统,在一定的条件下,将产生唯一一个全局渐近稳定的周期正解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定性的充分条件．     

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。     

一类带有肝炎B病毒感染的数学模型的全局稳定性分析

本文主要分析了一类具有肝炎B病毒感染且带有治愈率的典型的数学模型(HBV).通过稳定性分析,得到了该模型的无病平衡点与地方病平衡点全局稳定的充分条件,并且证明了当基本再生数R0＜1,HBV感染消失;当R0＞1,HBV感染持续.     

时滞传染病模型的指数稳定性

利用分析技巧研究了一类SEIRS传染病模型的动力学行为.结论表明如果再生数小于1,则带变时滞的传染病模型的无病平衡点是全局指数渐近稳定的,如果再生数大于1,得到传染病平衡点局部指数稳定的充分条件,同时给出了例子说明结论的有效性.     

一类带有肝炎B病毒感染的数学模型的全局稳定性分析（英文）

本文主要分析了一类具有肝炎B病毒感染且带有治愈率的典型的数学模型（HBV）.通过稳定性分析,得到了该模型的无病平衡点与地方病平衡点全局稳定的充分条件,并且证明了当基本再生数R0〈1, HBV感染消失;当R0〉1,HBV感染持续.     

相互干扰的捕食与被捕食者种群的Hassall模型定性分析

本文证明了Hassall模型的渐近稳定性、有界性、全局稳定性。解决了文献[1]对该模型的三个猜想：（1）模型在某种条件下,正平衡点（x^*,y^*）是渐近稳定的;（2）模型的一切正初始条件的解有界;（3）模型在一定条件下,正平衡点（x^*,y^*）是全局稳定的。     

捕食者有病的生态-流行病模型的分析

建立并分析了捕食者具有疾病且有功能反应的生态-流行病(SI)模型,讨论了解的有界性．应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。     

随机配对种群的两性模型的动力学性态

基于Kendall-Goodman模型，提出了一个两性具有不同生理性态的随机配对的两性模型．如果不考虑密度制约因素，那么模型存在一个全局渐近稳定的指数解；如果考虑密度制约因素，对于给定的一个出生函数，得到了唯一正平衡态存在及全局稳定的充要条件．结论表明，无论是否考虑密度制约因素，种群的性比总是稳定的．     

Mechanisms underpinning community stability along a latitudinal gradient: Insights from a niche-based approach

At large scales, the mechanisms underpinning stability in natural communities may vary in importance due to changes in species composition, mean abundance, and species richness. Here we link species characteristics (niche positions) and community characteristics (richness and abundance) to evaluate the importance of stability mechanisms in 156 butterfly communities monitored across three European countries and spanning five bioclimatic regions. We construct niche-based hierarchical structural Bayesian models to explain first differences in abundance, population stability, and species richness between the countries, and then explore how these factors impact community stability both directly and indirectly (via synchrony and population stability). Species richness was partially explained by the position of a site relative to the niches of the species pool, and species near the centre of their niche had higher average population stability. The differences in mean abundance, population stability, and species richness then influenced how much variation in community stability they explained across the countries. We found, using variance partitioning, that community stability in Finnish communities was most influenced by community abundance, whereas this aspect was unimportant in Spain with species synchrony explaining most variation; the UK was somewhat intermediate with both factors explaining variation. Across all countries, the diversity–stability relationship was indirect with species richness reducing synchrony which increased community stability, with no direct effects of species richness. Our results suggest that in natural communities, biogeographical variation observed in key drivers of stability, such as population abundance and species richness, leads to community stability being limited by different factors and that this can partially be explained due to the niche characteristics of the European butterfly assemblage.     

On the changing concept of evolutionary population stability as a reflection of a changing point of view in the quantitative theory of evolution

 Eighteen different terms, currently employed to define various concepts of evolutionary stability in population dynamics are mentioned in this paper. Most of these terms are used in different connotations and even different meanings by different authors. On the other hand, different terms are often employed by different authors to define quite the same concept. Twenty-five years ago there was only one, well-defined, concept of stability, universally recognized in the field. In this paper I will try to relate the recent confusion, concerning concepts of population stability, with a more serious, though not that well-recognized, confusion in the modern analytic approach to population dynamics and quantitative evolution. Concepts of population stability will be examined in relation to each other on the one hand and, on the other hand, in relation to two dichotomies regarding the dynamic processes to which they correspond: Short-term versus long-term processes and processes concerning phenotypic changes versus process concerning genotypic changes. A hopefully more consistent use of the current terminology is suggested. Received 15 August 1993; received in revised form 15 September 1994     

Mycorrhizal suppression and phosphorus addition influence the stability of plant community composition and function in a temperate steppe

Nutrient enrichment can reduce ecosystem stability, typically measured as temporal stability of a single function, e.g. plant productivity. Moreover, nutrient enrichment can alter plant–soil interactions (e.g. mycorrhizal symbiosis) that determine plant community composition and productivity. Thus, it is likely that nutrient enrichment and interactions between plants and their soil communities co-determine the stability in plant community composition and productivity. Yet our understanding as to how nutrient enrichment affects multiple facets of ecosystem stability, such as functional and compositional stability, and the role of above–belowground interactions are still lacking. We tested how mycorrhizal suppression and phosphorus (P) addition influenced multiple facets of ecosystem stability in a three-year field study in a temperate steppe. Here we focused on the functional and compositional stability of plant community; functional stability is the temporal community variance in primary productivity; compositional stability is represented by compositional resistance, turnover, species extinction and invasion. Community variance was partitioned into population variance defined as community productivity weighted average of the species temporal variance in performance, and species synchrony defined as the degree of temporal positive covariation among species. Compared to treatments with mycorrhizal suppression, the intact AM fungal communities reduced community variance in primary productivity by reducing species synchrony at high levels of P addition. Species synchrony and population variance were linearly associated with community variance with the intact AM fungal communities, while these relationships were decoupled or weakened by mycorrhizal suppression. The intact AM fungal communities promoted the compositional resistance of plant communities by reducing compositional turnover, but this effect was suppressed by P addition. P addition increased the number of species extinctions and thus promoted compositional turnover. Our study shows P addition and AM fungal communities can jointly and independently modify the various components of ecosystem stability in terms of plant community productivity and composition.     

Diversity-dependent stability under mowing and nutrient addition: evidence from a 7-year grassland experiment

Anthropogenic perturbations may affect biodiversity and ecological stability as well as their relationships. However, diversity-stability patterns and associated mechanisms under human disturbances have rarely been explored. We conducted a 7-year field experiment examining the effects of mowing and nutrient addition on the diversity and temporal stability of herbaceous plant communities in a temperate steppe in northern China. Mowing increased population and community stability, whereas nutrient addition had the opposite effects. Stability exhibited positive relationships with species richness at population, functional group and community levels. Treatments did not alter these positive diversity-stability relationships, which were associated with the stabilising effect of species richness on component populations, species asynchrony and portfolio effects. Despite the difficulty of pinpointing causal mechanisms of diversity-stability patterns observed in nature, our results suggest that diversity may still be a useful predictor of the stability of ecosystems confronted with anthropogenic disturbances.     

Analysis of a dengue disease transmission model

A model for the transmission of dengue fever in a constant human population and variable vector population is discussed. A complete global analysis is given, which uses the results of the theory of competitive systems and stability of periodic orbits, to establish the global stability of the endemic equilibrium. The control measures of the vector population are discussed in terms of the threshold condition, which governs the existence and stability of the endemic equilibrium.     

Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.     

金融稳定性与生态稳定性

亚洲金融危机以后,世界各国评估和诊断金融体系稳健程度的实务性研究取得了很大进展,但金融稳定性问题的理论研究仍相对滞后.本文讨论了用生态稳定性思想方法研究金融稳定性问题.文章先比较了金融稳定性的概念和生态学中有关稳定性的概念的异同,把生态稳定性概念移植、引申到金融系统中,建立了金融群落数学模型,给出了金融群落金融稳定的定义,论证了金融种群确定模型和随机模型的稳定性,介绍了金融群落随机模型的稳定性,最后分析了金融群落等级结构的稳定性.     

Selection and segregation distortion in a sex-differentiated population

We extend the classical model for selection at an autosomal locus in a sex-differentiated population to include segregation distortion. The equations remain the same, but the fitness parameters are interpreted differently and refer to alleles instead of genotypes. We derive conditions for internal and external stability of the equilibria, i.e., stability with respect to perturbations of alleles that are already present at equilibrium and stability with respect to invasion attempts by newly arising alleles. We show that, in a sex-differentiated population, external stability of an equilibrium can be judged on the basis of Shaw--Mohler criteria. Throughout, we compare the situation in populations with and without sex differentiation. Interestingly, internal stability is more difficult to achieve in a population without sex differentiation than in a population in which selection and segregation distortion are restricted to one sex. In a companion paper we show how the general results of the present paper can lead to new insights into specific systems such as the t complex of the house mouse.     

Global stability in a delayed partial differential equation describing cellular replication

Here we consider the dynamics of a population of cells that are capable of simultaneous proliferation and maturation. The equations describing the cellular population numbers are first order partial differential equations (transport equations) in which there is an explicit temporal retardation as well as a nonlocal dependence in the maturation variable due to cell replication. The behavior of this system may be considered along the characteristics, and a global stability condition is proved.     

Nitrogen enrichment weakens ecosystem stability through decreased species asynchrony and population stability in a temperate grassland

Biodiversity generally promotes ecosystem stability. To assess whether the diversity–stability relationship observed under ambient nitrogen (N) conditions still holds under N enriched conditions, we designed a 6‐year field experiment to test whether the magnitude and frequency of N enrichment affects ecosystem stability and its relationship with species diversity in a temperate grassland. Results of this experiment showed that the frequency of N addition had no effect on either the temporal stability of ecosystem and population or the relationship between diversity and stability. Nitrogen addition decreased ecosystem stability significantly through decreases in species asynchrony and population stability. Species richness was positively associated with ecosystem stability, but no significant relationship between diversity and the residuals of ecosystem stability was detected after controlling for the effects of the magnitude of N addition, suggesting collinearity between the effects of N addition and species richness on ecosystem stability, with the former prevailing over the latter. Both population stability and the residuals of population stability after controlling for the effects of the magnitude of N addition were positively associated with ecosystem stability, indicating that the stabilizing effects of component populations were still present after N enrichment. Our study supports the theory predicting that the effects of environmental factors on ecosystem functioning are stronger than those of biodiversity. Understanding such mechanisms is important and urgent to protect biodiversity in mediating ecosystem functioning and services in the face of global changes.