关于人口发展方程半离散算法的研究

利用半离散的方法将人口发展方程的边界条件进行离散,离散后得到两个相应的偏微分方程模型,然后利用算子半群的理论证明了离散后的解都逼近原方程的解,从而证明这种半离散方法是可行的.     

GLOBAL SIMPLE WAVE SOLUTIONS TO A KIND OF TWO DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS

This paper is concerned with the simple waves of a kind of two dimensional hyperbolic system of conservation laws, which can be obtained from the two dimensional relativistic membrane equation in Minkowski space. Using wave decomposition method, we get that a flow adjacent to a nonconstant state can be a global simple wave. Furthermore, the flow is covered by three families of characteristics, in which the first family of characteristics is straight and the others are curved, which is different to the almost related results.     

基于灰色马尔可夫链模型的人口预测

将灰色预测模型和马尔可夫链预测相结合,将其应用到人口预测中,并依据南京市历年总人口数据进行计算,可以比较准确地预测2008年的户籍人口数,验证了其有效性;同时由模型可以预测2010年,2011年南京户籍人口数以做参考用,灰色马尔可夫链可视为人口预测的可行且有效的方法。     

A density-dependent model describing age-structured population dynamics using hawk–dove tactics

In this paper we deal with a nonlinear two-timescale discrete population model that couples age-structured demography with individual competition for resources. Individuals are divided into juvenile and adult classes, and demography is described by means of a density-dependent Leslie matrix. Adults compete to access resources; every time two adults meet, they choose either being aggressive (hawk) or non-aggressive (dove) to get the best pay-off. Individual encounters occur much more frequently than demographic events, what yields that the model takes the form of a two-timescale system. Approximate aggregation methods allow us to reduce the system while preserving at the same time crucial asymptotic information for the whole population. In this way, we are able to describe the total population size as function of individual aggressiveness level and environmental richness. Model analysis shows a general trend with species that look for richer environment having smaller proportions of hawk individuals with larger costs.     

An efficient numerical method for singular perturbation problems

In this paper, we propose a method for the numerical solution of singularly perturbed two-point boundary-value problems (BVPs). First, we develop two schemes to integrate initial–value problem (IVP) for system of two first-order differential equations, and then by using these schemes we solve the BVP. Precisely, we convert the second-order BVP into a system of first-order differential equations, and then apply the numerical schemes to obtain the solution. In order to get an initial condition for the system, we use the asymptotic approximate solution. Error estimates are derived and numerical examples are provided to illustrate the present method.     

On a new model of two-patch predator-prey system with migration of both species

In this paper we explore the dynamics of predator-prey in a two patch system. The two patches of the system are coupled with both the migration of the predator and the prey. The purpose of this exploration is to find upper and lower bounds for the populations and get an insight on the different possibilities with the three types of Holling functional responses. Also we discuss the stability and instability of the equilibrium solutions found in earlier papers. Numerical simulations are provided to graphically demonstrate the population dynamics of the system.     

Modelling on fuzzy control systems

A kind of modelling method for fuzzy control systems is first proposed here, which is called modelling method based on fuzzy inference (MMFI). It should be regarded as the third modelling method that is different from two well-known modelling methods, that is, the first modelling method, mechanism modelling method (MMM), and the second modelling method, system identification modelling method (SIMM). This method can, based on the interpolation mechanism on fuzzy logic system, transfer a group of fuzzy inference rules describing a practice system into a kind of nonlinear differential equation with variable coefficients, called HX equations, so that the mathematical model of the system can be obtained. This means that we solve the difficult problem of how to get a model represented as differential equations on a complicated or fuzzy control system.     

具有两个状态的修复系统的指数稳定性

利用C0-半群理论证明了具有两个状态的可修复系统非负解的存在唯一性,并研究了相应算子的谱特征,通过分析本质谱界经过扰动后的变化,得到系统动态解以指数形式收敛于稳态解.     

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.     

一类非线性耦合双曲型方程组的研究

研究了一类非线性耦合双曲型方程组初边值问题,讨论了初边值条件以及非线性项中指数满足的条件,利用Galerkin方法和紧致性的结果,以及椭圆型方程解的正则性定理,经过严格的推导证明了该问题解的存在唯一性的若干结果.     

正规升列在参数代数方程组求解中的应用

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法．对于给定的的代数方城组,通过正规分解,可以得到一组具有三角形式的分解．根据这种三角形式,我们可以给出代数方程组的所有解．而对于带有参数方程组,将给出方程组有解时参数需满足的条件．进一步,对于给定的参数值,正规分解中得到三角形式仍然保持,通过求解三角形式的方程组从而得出原参数方程组的解．     

速效感冒片中扑热息痛与咖啡因含量测定的一种新方法

扑热息痛和咖啡因是速效感冒片中的主要成分,其含量决定了速效感冒片的药效及副作用的大小.我们通过实验分别做出一定浓度扑热息痛溶液和咖啡因溶液的紫外吸光度随检测波长的变化曲线(λ-A曲线),并用M athem acica软件中曲线拟合的方法分别求出上述两条变化曲线的拟合方程,以这两个方程的线性组合形式拟合速效感冒片溶液紫外光谱的λ-A曲线,根据系数的比例关系求得扑热息痛和咖啡因在速效感冒片中的含量.简化了传统双波长法的操作,提高了检测速度.     

General conditions for global stability in a single species population-toxicant model

We deal with the global stability for a well-known population-toxicant model. We make use of a geometrical approach to the global stability analysis for ordinary differential equation which is based on the use of a higher-order generalization of the Bendixson's criterion. We obtain sufficient conditions for the global stability of the unique nontrivial equilibrium. These conditions are expressed in terms of a generic functional describing the population dynamics. In the special case of a logistic-like population dynamics, we get conditions which improve the ones previously known, obtained by means of the Lyapunov direct method.     

广义Захаров方程组的初边值问题

本文用积分估计的方法对于一类更广泛的Захаров方程组的初边值问题（其中一维问题为第三初边值问题，二维为第一初边值问题），证明了广义解的存在性。     

Modelling and bifurcation analysis of internal cantilever beam system on a steadily rotating ring

Using Hamilton variation principle, a nonlinear dynamic model of the system with a finite deforming Rayleigh beam clamped radially to the interior of a rotating rigid ring, under the assumption that the constitutive relation of the beam is linearly elastic, is discussed. The bifurcation behavior of the simple system with the Euler-Bernoulli beam is also discussed. It is revealed that these two models have no influence on the critical bifurcation value and buckling solution in the steady state. Then we use the assumption model method to analyse the bifurcation behavior of the steadily rotating Euler-Bernoulli beam and get two different types of bifurcation behavior which physically exist. Finite element method and shooting method are used to verify the analytical results. The numerical results confirm our research conclusion. Project supported by the National Natural Science Foundation of China (Grant No. 19332022) and Space High Technology Foundation of China.     

A high order finite difference method with Richardsonextrapolation for 3D convection diffusion equation

In this paper, we extend the Sun and Zhang’s [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on the fine and the coarse grids. Then, we use the Richardson extrapolation technique by combining the two approximate solutions to get a sixth order accurate solution on coarse grid. Finally, we apply an operator interpolation scheme to achieve the sixth order accurate solution on the fine grid. During this process, we use alternating direction implicit (ADI) method to solve the resulting linear systems. Numerical experiments are conducted to verify the accuracy and effectiveness of the present method.     

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of convection-diffusion type of third order Ordinary Differential Equations (ODEs) in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. In order to get a numerical solution for the derivative of the solution, the domain is divided into two regions namely inner region and outer region. The shooting method is applied to the inner region while standard finite difference scheme (FD) is applied for the outer region. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing.     

Banach空间中带Poisson跳的随机种群方程的数值分析

本文研究Banach空间中带Poisson跳的随机种群方程,通过离散使之成为随机微分方程,进而运用显式Euler公式来分析其数值解与解析解的误差.     

宏观经济分布参数系统的临界值问题

本文把经济系统作为一类生灭过程来考虑 .应用人口控制论和森林系统的成功经验 ,研究经济系统的临界值问题 .首先 ,基于实际的经济分析、预测模型 ,在宏观层次上建立经济系统的控制模型 .连续模型便于理论研究 ,离散模型便于计算机仿真 .然后在这个控制模型的基础上 ,寻找使国民经济持续发展所需要的最小资产积累率表达形式 .本文得到的理论值将帮助我们更深刻地理解经济系统     

Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders.