离散型单种群扩散模型的全局渐近稳定性

本文研究离散单种扩散模型全局渐近稳定性,利用单调算子和凹算子的理论讨论了其全局渐近稳定性,并得到了正平衡点全局渐的稳定和物种绝灭的充分条件。     

具有垂直传染和时滞的肺结核传染病模型

建立了一类含时滞具有垂直传染的肺结核传染病模型,得到了系统的基本再生数R_0.利用平衡点处的特征方程讨论平衡点的局部渐近稳定性;通过构造Lyapunov函数讨论地方病平衡点的全局渐近稳定性;运用比较定理和分析的方法得到无病平衡点的全局渐近稳定性和地方病平衡点的持久性;最后利用数值模拟分析了时滞在模型中的影响.     

具有时滞和避难所的捕食者-两共存食饵模型

研究了一类具有时滞和避难所的捕食-被捕食模型的一致持久性和全局稳定性.利用比较原理讨论了模型的一致持久性,运用Lyapunov函数方法得到了模型全局渐近稳定的充分条件.     

潜伏期具有传染性的SEIRS流行病模型的全局稳定性

研究一类潜伏期和染病期均具有传染性和康复可能的SEIRS流行病模型,确定了疾病流行与否的阈值,利用Routh-Hurwitz判据和LaSalle不变集原理得到无病平衡点的全局渐近稳定性,并借助广义Bendixson-Dulac定理得到地方病平衡点的全局渐近稳定性,最后给出数值模拟.     

具有Crowley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性（英文）

本文讨论了一类具有Growley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性.利用Lyapunov函数和LaSalle不变原理证明:当基本再生数R_0≤1时,无病平衡点全局渐近稳定;当基本再生数R_01且免疫基本再生数R_0≤1时,免疫平衡点全局渐近稳定;当R_01时,地方病平衡点全局渐近稳定.     

一类捕食者与被捕食者模型的持久性与稳定性

研究了一类捕食者与被捕食者模型,该生态系统是一个食饵种群被一个捕食种群捕食.当给定参数满足一定条件下,利用比较原理和构造Lyapunov函数的方法,证明了系统的持久性和全局渐近稳定性,并讨论了正平衡点的渐近稳定性.     

具有比率依赖型功能反应函数的食饵-捕食者征税模型分析

本文研究了一个具有功能反应函数的食饵一捕食者征税模型，得到了该系统正平衡点的存在性、局部渐近稳定性和全局渐近稳定性的条件，并利用Pontrjagin最大值原理得到了最优税收策略．该文为资源管理者制定合理的管理政策提供理论依据．     

出生和死亡具有密度制约的不育控制下的害鼠种群动态

讨论了一类出生和死亡都具有密度制约的不育单种群害鼠模型,得到了各平衡点存在及局部渐近稳定的条件,证明了各平衡点的全局渐近稳定性.最后利用数值模拟验证了所得结论,并进一步分析了密度制约因素和传染率对于平衡点的稳定性及种群规模的影响.     

一类带有隔离和分布时滞的SIQRS的传染病模型的稳定性分析

提出一类含有分布时滞和隔离的传染病模型,利用构造李亚普诺夫泛函的方法,得到无病平衡点和地方平衡点全局渐近稳定性的结论,并讨论了永久免疫时,系统无病平衡点的指数稳定性.     

随机Lotka-Volterra系统的稳定性

利用Lyapunov方法与K．lto公式及鞅的理论,研究了随机Lotka-Volterra系统正平衡点的全局渐近稳定性．得到了随机全局渐近稳定的主要定理,并以确定性系统的全局稳定性作为定理的推论．     

Global stability of population models

Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.     

Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic

In this paper, a nonlinear model for genetic regulator networks (GRNs) with SUM regulatory logic is presented. Four sufficient and necessary conditions of global asymptotical stability and global exponential stability for the equilibrium point of the GRNs are proposed, respectively. Specifically, three weak sufficient conditions and corresponding corollaries are derived by using comparing theorem and Dini derivative method. Then, a famous GRN model is used as the example to illustrate the effectiveness of our theoretical results. Comparing to the results in the previous literature, some novel ideas, study methods and interesting results are explored.     

Conserved quantitative stability/flexibility relationships (QSFR) in an orthologous RNase H pair

Many reports qualitatively describe conserved stability and flexibility profiles across protein families, but biophysical modeling schemes have not been available to robustly quantify both. Here we investigate an orthologous RNase H pair by using a minimal distance constraint model (DCM). The DCM is an all atom microscopic model [Jacobs and Dallakyan, Biophys J 2005;88(2):903-915] that accurately reproduces heat capacity measurements [Livesay et al., FEBS Lett 2004;576(3):468-476], and is unique in its ability to harmoniously calculate thermodynamic stability and flexibility in practical computing times. Consequently, quantified stability/flexibility relationships (QSFR) can be determined using the DCM. For the first time, a comparative QSFR analysis is performed, serving as a paradigm study to illustrate the utility of a QSFR analysis for elucidating evolutionarily conserved stability and flexibility profiles. Despite global conservation of QSFR profiles, distinct enthalpy-entropy compensation mechanisms are identified between the RNase H pair. In both cases, local flexibility metrics parallel H/D exchange experiments by correctly identifying the folding core and several flexible regions. Remarkably, at appropriately shifted temperatures (e.g., melting temperature), these differences lead to a global conservation in Landau free energy landscapes, which directly relate thermodynamic stability to global flexibility. Using ensemble-based sampling within free energy basins, rigidly, and flexibly correlated regions are quantified through cooperativity correlation plots. Five conserved flexible regions are identified within the structures of the orthologous pair. Evolutionary conservation of these flexibly correlated regions is strongly suggestive of their catalytic importance. Conclusions made herein are demonstrated to be robust with respect to the DCM parameterization.     

Mathematical model of anaerobic digestion in a chemostat: effects of syntrophy and inhibition

Three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis are described by a system of differential equations modelling the interaction of microbial populations in a chemostat. The microbes consume and/or produce simple substrates, alcohols and fatty acids, acetic acid, and hydrogen. Acetogenic bacteria and hydrogenotrophic methanogens interact through syntrophy. The model also includes the inhibition of acetoclastic and hydrogenotrophic methanogens due to sensitivity to varying pH-levels. To examine the effects of these interactions and inhibitions, we first study an inhibition-free model and obtain results for global stability using differential inequalities together with conservation laws. For the model with inhibition, we derive conditions for existence, local stability, and bistability of equilibria and present a global stability result. A case study illustrates the effects of inhibition on the regions of stability. Inhibition introduces regions of bistability and stabilizes some equilibria.     

一类具连续时滞的三种群互助模型正平衡态的渐近稳定性

本文研究了一类具连续时滞的三种群互助模型，利用上、下解方法及相应的单调迭代方法，获得了该系统存在唯一正常数平衡态及该平衡态是全局渐近稳定的结论，为讨论时滞三种群模型提供了一种有效方法，所得结果也适用于二种群互助模型及不含时滞和扩散项的互助模型，因而推广了已有的一些结论．     

分布时滞竞争模型的周期解

研究了分布时滞竞争模型周期解,利用Gaines与Mawhin的重合度理论,通过构造恰当的Lyapunov函数得到模型正周期解的存在性、唯一性及全局稳定性。     

Weak trophic interactions and the balance of enriched metacommunities

Weak trophic interactions have been shown to promote the stability of ecological food webs characterized by perfect mixing. However, their importance at the landscape level and response to enrichment has not been extensively examined. In this paper we examine the food-web model explored by McCann et al. [1998. Weak trophic interactions and the balance of nature. Nature 395, 794-798]. The model is expanded into a metacommunity construct where local communities are coupled through global or local dispersal. We analyze global and local stability, as well as spatial synchrony in relation to trophic interaction strength and dispersal regimes. Results reveal that weak interactions can operate through two scale-dependent mechanisms: (i) under low local dispersal regimes, local stabilization of each community under weak interactions directly scales-up to global stability. (ii) Under high local dispersal, asynchronous local destabilization associated with weak interactions proves the driver behind global stability. In the face of enrichment, weak trophic interactions are shown to be instrumental in promoting global stability when dispersal is local. These results demonstrate how the importance of weak trophic interactions can be generalized at the landscape level despite contrary local predictions.     

一类疫苗预防接种具有效期性的SIRS模型稳定性分析

研究了一类预防接种下疫苗具有有效期的SIRS传染病模型,得到了决定疾病绝灭与否的闽值,给出了无病平衡点和地方病平衡点的全局稳定性的充分条件,最后借助Matlab软件进行了数值模拟．