一类具有非线性密度制约的食饵-捕食者扩散模型的稳定性

讨论了一类具有非线性密度制约的食饵-捕食者扩散规模型,运用线性化方法和Lyapunov函数法分别讨论该反应扩散模型唯一正平衡点的局部渐近稳定性和全局渐近稳定性.     

具有非单调传染率的SIQR传染病模型的稳定性分析

该文研究了一类具有非单调传染率的SIQR传染病模型,讨论了平衡点的存在性,运用特征值法、Hurwit判据和极限方程理论证明了当阈值R_01时无病平衡点是全局渐近稳定的;当R_01时,无病平衡点是不稳定的.并采用Lipunov函数法和Lasalle不变性原理证明了地方性平衡点是全局渐近稳定的.最后进行了数值模拟,验证了理论结果的有效性.     

时标上脉冲混合动态系统实用渐近稳定性（英文）

在此篇论文中,采用Lyapunov直接法研究了一类时标脉冲混合动态系统关于两个测度的实用稳定性,进而将多个Lyapunov函数法推广到实用渐近稳定的研究中,并得到了相应的结论.     

具有脉冲效应的非自治Lotka-Valterra竞争系统的持久性和渐近行为

本文考虑了两种群具有脉冲效应的非自治Lotka-Valterra竞争系统．运用比较定理和李雅普诺夫函数法,建立了系统的持久性和渐近行为的充分条件．     

广义Logistic模型奇摄动问题的渐近分析

本文讨论了一类具有慢变参数的广义Logistic模型的渐近性态.首先,用匹配法构造了其渐近近似解,其次运用上下解法对近似解的一致有效性进行了证明,并给出了近似解与精确解之间的误差估计.最后,通过几个例子将所求近似解与精确解进行了比较,表明了文中方法的有效性.     

渐近周期的Logistic方程

主要研究了渐近周期的Logistic方程,得到了渐近周期解的存在唯一性,全局吸引性;进一步得到渐近周期函数对加减乘除,导数,微分,复合函数运算的封闭性;渐近周期函数空间是Banach空间,并得到高维系统下的渐近周期函数空间是Banach空间．     

综述: 渐近优先性及其机制

对渐近信号的优先加工被称为渐近优先性,该效应普遍存在于人类和动物的视觉、听觉和跨感觉通道中.人类神经影像学研究发现负责加工渐近信号的脑区涉及一个大规模相互协作和沟通的分布式神经网络,包括颞上沟、颞顶叶连接处以及一些运动区.对多种动物的细胞水平研究也发现了对渐近信号选择性敏感的神经元和神经通路.威胁论、注意捕获理论和自动加工理论从不同角度解释了渐近优先性产生的原因.未来研究可进一步考察刺激的社会、情绪等属性对渐近优先性的影响,探索多通道渐近渐远信息的整合和注意分配机制.     

渐近优先性及其机制

对渐近信号的优先加工被称为渐近优先性,该效应普遍存在于人类和动物的视觉、听觉和跨感觉通道中.人类神经影像学研究发现负责加工渐近信号的脑区涉及一个大规模相互协作和沟通的分布式神经网络,包括颞上沟、颞顶叶连接处以及一些运动区.对多种动物的细胞水平研究也发现了对渐近信号选择性敏感的神经元和神经通路.威胁论、注意捕获理论和自动加工理论从不同角度解释了渐近优先性产生的原因.未来研究可进一步考察刺激的社会、情绪等属性对渐近优先性的影响,探索多通道渐近渐远信息的整合和注意分配机制.     

离散型二维竞争系统的渐近稳定性

研究了离散型二维竞争系统的渐近稳定性,得到了这类生物模型关于正平衡点渐近稳定的一系列充分条件。     

具反馈控制的时滞阶段结构种群模型的稳定性

研究具反馈控制的时滞阶段结构种群模型,证明了正平衡点的局部渐近稳定性, 并给出了正平衡点全局渐近稳定的充分条件．     

Spectral properties of Eigen evolution matrices

Eigen [7] has employed deterministic kinetic-like equations to describe macromolecular replication and mutation leading to selection. The solutions to these equations and their physically interesting properties depend upon the spectrum of a type of matrix appearing in those equations. Below we explicitly solve for the spectrum of a fairly general class of such matrices. These solutions are obtained recursively for equations describing macromolecules of any length v.     

The drift approximation solves the Poisson, Nernst-Planck, and continuum equations in the limit of large external voltages

Nearly linear current-voltage curves are frequently found in biological ion channels. Using the drift limit of the substantially non-linear Poisson-Nernst-Planck equations, we explain such behavior of diffusion-controlled charge transport systems. Starting from Gauss' law, drift, and continuity equations we derive a simple analytical current-voltage relation, which accounts for this deviation from linearity. As shown previously, the drift limit of the Nernst-Planck equation applies if the total electric current is dominated by the electric field, and integral contributions from concentration gradients are small. The simple analytical form of the drift current-voltage relations makes it an ideal tool to analyze experiment current-voltage curves. We also solved the complete Poisson-Nernst-Planck equations numerically, and determined current-voltage curves over a wide range of voltages, concentrations, and Debye lengths. The simulation fully supports the analytical estimate that the current-voltage curves of simple charge transport systems are dominated by the drift mechanism. Even those relations containing the most extensive approximations remained qualitatively within the correct order of magnitude. Received: 24 September 1998 / Revised version: 22 January 1999 / Accepted: 22 January 1999     

Capturing the interaction types of two Bt toxins Cry1Ac and Cry2Ab on suppressing the cotton bollworm by using multi‐exponential equations

Transgenic crops are increasingly promoted for their practical effects on suppressing certain insect pests, but all transgenic crops are not equally successful. The insect pests can easily develop resistance against single Bacillus thuringiensis (Bt) toxin transgenic crops. Therefore, transgenic crops including two or more mixed Bt‐toxins can solve this problem by delaying the resistance development and killing the majority of targeted pests before the evolution of resistance. It is important to test the controlling effects of transgenic crops including multiple mixed toxins on a particular insect pest. Previous research has checked the cross‐resistance and interactions between Bt toxins Cry1Ac and Cry2Ab against one susceptible and four resistant strains of cotton bollworm. The results showed that independence was the main interaction type between two toxins for the susceptible strain, whereas synergism was the main interaction type for any one resistant strain. However, the optimal combinations of two toxins were not obtained. In the present study, we developed two multi‐exponential equations (namely bi‐ and tri‐exponential equations) to describe the combination effects of two Bt toxins. Importantly, the equations can provide predictions of combination effects of different continuous concentrations of two toxins. We compared these two multi‐exponential equations with the generalized linear model (GLM) in describing the combination effects, and found that the bi‐ and tri‐exponential equations are better than GLM. Moreover, the bi‐exponential equation can also provide the optimal dose combinations for two toxins.     

Asymptotic velocity of one dimensional diffusions with periodic drift

We consider the asymptotic behavior of the solution of one dimensional stochastic differential equations and Langevin equations in periodic backgrounds with zero average. We prove that in several such models, there is generically a non-vanishing asymptotic velocity, despite of the fact that the average of the background is zero.      

Fractional Reproduction-Dispersal Equations and Heavy Tail Dispersal Kernels

Reproduction-Dispersal equations, called reaction-diffusion equations in the physics literature, model the growth and spreading of biological species. Integro-Difference equations were introduced to address the shortcomings of this model, since the dispersal of invasive species is often more widespread than what the classical RD model predicts. In this paper, we extend the RD model, replacing the classical second derivative dispersal term by a fractional derivative of order 1相似文献   

Dispersal and competition models for plants

New models for seed dispersal and competition between plant species are formulated and analyzed. The models are integrodifference equations, discrete in time and continuous in space, and have applications to annual and perennial species. The spread or invasion of a single plant species into a geographic region is investigated by studying the travelling wave solutions of these equations. Travelling wave solutions are shown to exist in the single-species models and are compared numerically. The asymptotic wave speed is calculated for various parameter values. The single-species integrodifference equations are extended to a model for two competing annual plants. Competition in the two-species model is based on a difference equation model developed by Pakes and Maller [26]. The two-species model with competition and dispersal yields a system of integrodifference equations. The effects of competition on the travelling wave solutions of invading plant species is investigated numerically.     

Pair formation models with maturation period

The standard model for pair formation is generalized to include a maturation period. This model in the form of three coupled delay equations is a special case of the general age-structured model for a two-sex population. The exact conditions for the existence of an exponential (persistent) two-sex solution are derived. It is shown that this solution is unique and locally stable. In order to achieve these results the theory of homogeneous differential equations is extended to a class of homogeneous delay equations.     

三参数增长模型拟合:以季风常绿阔叶林中两个优势乔木种群为例

Logistic、Mitscherlich、Gompertz方程是一类三参数饱和增长曲线模型,广泛地应用于许多学科领域．本文基于logistic方程饱和值K估计的三点法、四点法,推导出Mitscherlich、Gompertz方程K值的三点法、四点法估计公式,并以南亚热带季风常绿阔叶林中两种优势乔木厚壳桂、黄果厚壳桂种群为例,先用三点法或四点法估计出K值,再通过线性回归与非线性回归相结合的方法,可获得三个增长模型中三个参数的最优无偏估计．实例研究表明,两个优势种群增长数据均符合三个增长模型,但更符合增长曲线呈S形的logistic、Gompertz方程,且以logistic方程最适合于观察;黄果厚壳桂种群增长快于厚壳桂种群．     

回归方程法测定紫荆叶面积的比较研究

以紫荆成熟叶片为材料,建立起紫荆的叶面积与其叶长、叶宽、以及叶长×叶宽之间的和幂函数、指数函数、线性回归方程。结果表明,叶长与叶面积、叶宽与叶面积、叶长宽积与叶面积的幂函数、指数函数、线性函数均呈正相关关系。9个回归方程均可用于测算紫荆的叶面积,其中以叶长宽积和叶面积的线性方程测算结果更为精确。     

等熵方程与生物熵限方程

本文分析了等熵方程;推导出核酸序列的熵限方程,率先提出了生物进化过程中核酸序列选择的熵原则;绘制了分析核酸序列熵变的等熵图．