三种群互惠模型抛物系统解的整体存在与爆破

研究了三种群互惠模型的抛物系统,用上下解方法研究解的整体存在性与爆破问题,并给出了相应的条件.结果表明当种群自身的竞争强时解整体存在,反之则有可能爆破.     

强耦合竞争-竞争-互惠模型古典解的整体存在性

应用能量估计方法和bootstrap技巧证明了一类强耦合反应扩散方程系统在任意维空间中古典解的整体存在性,该系统是竞争种群含自扩散和交错扩散,互惠种群仅含自扩散的竞争-竞争-互惠模型．     

竞争-竞争-互惠交错扩散模型古典解的整体存在性

应用一些Banach空间之间较详细的插值结果,讨论了竞争-竞争-互惠交错扩散模型古典解的整体存在性.     

一类带时滞竞争模型的周期解

研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统．用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件．     

一个竞争模型的一致持续生存

本文研究一个带有时滞的竞争模型的一致持续生存。首先证明了离散时滞不影响种群的一致持续生存,接着在种群增长率是周期的假设下讨论了正周期解的存在性,最后给出了连续时滞模型一致持续生存的充分条件。     

带时滞互惠模型的稳定性和行波解的存在性

本文建立了一类空间非局部带时滞影响的互惠生物种群系统模型.前部分利用线性化方法证明了该模型的简单动力学行为,即证明了零平衡点和两个边界平衡点都是不稳定的,唯一的正平衡点是稳定的,同时还用Redlinger上下解方法得出了该模型的初边值问题存在唯一的正则解;后部分则证明了该反应扩散系统连接零平衡点和正平衡点的行波解的存在性.     

双营养Chemostat模型周期解的全局吸引性

研究含有时滞的双营养单种群Ｃｈｅｍｏｓｔａｔ模型周期解的全局吸引性,首先利用强正、凹算子理论给出了系统存在唯一正周期解的充分条件,然后利用泛函微分方程的单调理论得到了正周期解的全局吸引性。     

离散时间的互惠系统的正周期解的存在性

利用重合度理论中的延拓定理研究了一类具有周期系数的离散时间的差分互惠系统模型．得到了该系统正周期解存在的充分条件．     

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。     

具年龄结构和时滞的自食种群系统的周期解

利用延拓定理讨论具年龄结构和时滞的自食种群系统正周期解的存在性,得到周期解存在的条件,推广了已有结论.     

根表面养分吸收通量和根围溶质浓度的近似解析解

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Approximate analytical solutions of root surface nutrient uptake flux and rhizosphere solute concentrations

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

On the stability of separable solutions of a sexual age-structured population dynamics model

The Sharpe-Lotka-McKendrick-von Foerster equations for non-dispersing age-sex-structured populations with a harmonic mean type mating law are considered and their separable solutions are analysed. For certain forms of the demographic rates the underlying evolution equations are reduced to systems of ODEs, the long time behavior of their solutions is studied, and the stability of separable solutions is discussed. It is found that for the constant death rates and constant sex ratio of newborns with stationary birth rates this model admits one one-parameter class of separable solutions, two such classes (repeated or different) or no such ones. In the case of special forms of age-dependent birth rates, solutions of one of these two different classes corresponding to the greater root of the characteristic equation are locally stable, solutions of the other one corresponding to the smaller root are unstable, and the population dies out if the model does not admit separable solutions or if initial densities of newborns are small enough in the case of the existence of separable solutions. In the case of constant vital rates, the model has no separable solutions or admits only one class of such ones that are globally stable.     

Emergence of oscillations in a model of weakly coupled two Bonhoeffer-van der Pol equations

Bifurcations of periodic solutions in a model of weakly coupled two Bonhoeffer-van der Pol equations are studied. The model realizes a half-center model with reciprocal inhibition, a typical model used in the field of neural motor control to account for the generation of alternating rhythmic bursts observed in motoneurons and spinal neural networks. Several oscillatory solutions such as in-phase, anti-phase as well as out-of-phase solutions emerge from the model's equilibrium as one of the parameters of the model changes. Among the variety of bifurcations exhibited by the model, we analyze Hopf bifurcations, by which several periodic solutions emerge, and illustrate generation mechanisms of alternating oscillations in the model.     

Approximate expressions of the bifurcating periodic solutions in a neuron model with delay-dependent parameters by perturbation approach

This paper is interested in gaining insights of approximate expressions of the bifurcating periodic solutions in a neuron model. This model shares the property of involving delay-dependent parameters. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work so harder. Most existing methods for studying the nonlinear dynamics fail when applied to such a class of delay models. Although Xu et al. (Phys Lett A 354:126–136, 2006) studied stability switches, Hopf bifurcation and chaos of the neuron model with delay-dependent parameters, the dynamics of this model are still largely undetermined. In this paper, a detailed analysis on approximation to the bifurcating periodic solutions is given by means of the perturbation approach. Moreover, some examples are provided for comparing approximations with numerical solutions of the bifurcating periodic solutions. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only.     

A weakly nonlinear analysis of a model of avascular solid tumour growth

 In this paper we study a mathematical model that describes the growth of an avascular solid tumour. Our analysis concentrates on the stability of steady, radially-symmetric model solutions with respect to perturbations taken from the class of spherical harmonics. Using weakly nonlinear analysis, previous results are extended to show how the amplitudes of the asymmetric modes interact. Attention focuses on a special case for which the model equations simplify. Analysis of the simplified model equations leads to the identification of a two-parameter family of asymmetric steady solutions, the dimensions of whose stable and unstable manifolds depend on the system parameters. The asymmetric steady solutions limit the basin of attraction of the radially-symmetric steady state when it is linearly stable. On the basis of these numerical and analytical results we postulate the existence of fully nonlinear steady solutions which are stable with respect to time-dependent perturbations. Received: 25 October 1998 / Revised version: 20 June 1998     

一类具有时滞的微生物连续培养数学模型研究

研究了具有强核函数时滞的微生物连续培养数学模型,利用泛函微分方程理论和数值解法得到系统在一定操作条件下存在Hopf分叉以及分叉值随操作参数变化的规律,并研究了Hopf分叉产生的方向及周期解的稳定性,绘制了周期解的图形和相图.该模型定性地描述了实验中的振荡和过渡现象.最后与弱核函数时滞模型、离散时滞模型进行比较,分析了它们对多态、振荡等动态行为的影响。     

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.     

Thermal self-focusing during solar flares

By solving a nonlinear equation for a heat source with a power proportional to Т ^β (β > 1), it is shown that heat localization in the transverse cross section of a magnetic tube with a classical thermal conductivity occurs in the blowup regime in the form of microstructures—temperature background cells bounded by hot walls with a spatial scale of <100 m. The reduction in the integral X-ray emissivity observed on board of spacecrafts in the early stage of the flare is attributed to thermal self-focusing, i.e., a decrease in the factor of filling of the flare volume with hot plasma due to the narrowing of the hot walls of the microstructure.