具有脉冲扰动的随机周期单种群扩散模型(英文)

文章研究一个具有脉冲与随机扰动的周期单种群扩散模型.通过构建合适的Lyapunov函数及利用脉冲微分方程比较定理与随机微分方程比较定理,获得种群灭绝和平均持续生存的条件.进而我们确定系统解的均值上界条件.     

具脉冲扩散效应的单种群动力学模型

讨论了两斑块间脉冲扩散的单种群动力学模型,利用离散动力系统频闪映射理论,得到了种群持续生存的充分条件．结论31,1~了现实的生物种群动力学性质,也丰富了脉冲微分方程理论．     

固定周期脉冲微分方程到状态依赖脉冲的转化及应用

本文研究了一类二维状态依赖脉冲微分方程的阶1周期解存在性和轨道稳定性条件．然后,将一维固定周期脉冲的微分方程转化为二维状态依赖脉冲微分方程,研究其阶一周期解的存在性和稳定性．作为应用,我们研究了固定周期常数收获的Logistic方程的动力学性质,以及两个固定周期注射药物单室扩散模型的动力学性质．     

具脉冲收获与脉冲单边扩散的单种群动力学模型研究

建立了一类具脉冲收获与脉冲单边扩散在不同固定脉冲时刻的单种群动力学模型利用离散动力系统频闪映射理论,得到了脉冲收获的阈值.该结论说明只要收获量不超过其阈值通过扩散则种群可以保持持续生存.     

一个生物种群非线性泛函微分方程模型整体解的聚集性

自然界的种群,如鱼类、鸟类和有蹄兽类有聚集成群的现象,研究种群的聚集性是生物数学中的一个有趣的课题．本文讨论了一个有关生物种群的非线性泛函微分方程模型整体解的聚集性和稳定性问题．     

一类单种群增长模型正解的振动性

利用一种新的方法研究了一类单种群增长模型—时滞微分方程N(t)=的解关于其正平衡点N=1的振动性,所获结果改进了已有文献中的相关结论。     

具脉冲出生单种群模型的脉冲收获阈值分析

讨论了与生物资源管理相关的具脉冲出生与脉冲收获的单种群动力学模型,利用离散动力系统频闪映射理论,得到了生物资源管理控制阈值的充分条件.结论为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲微分方程理论.     

具小扩散率种群的生长和灭绝行为

本文研究一类由反应扩散系统的初边问题描述的具常投放率的捕食食饵种群的生长模型,应用上、下解理论分析其解的长时间性态和具小扩散率种群的灭绝行为,给出参数环境．     

非线性种群反应扩散系统的奇摄动

研究了一类具有非线性种群反应扩散系统奇摄动问题,在适当的条件下,利用微分不等式理论,讨论了问题解的存在性和渐近性态．     

扩散系数依赖生态资源丰富度的单种群扩散模型

研究了一个扩散系数依赖生态资源丰富度的单种群脉冲扩散模型.利用单调凹算子理论,证明了在一定条件下,系统存在唯一全局渐近稳定的正周期解.通过数值模拟,验证了理论结果.结论表明,迁移有利于斑块环境下白头叶猴种群的持续生存.     

脉冲浮游生物植化相克模型解的渐近行为

讨论了一类在周期变化环境中的浮游生物植化相克的竞争模型．模型由一个修正的周期系数Lotka-Volterra竞争模型及一些周期脉冲作用条件描述．利用脉冲微分方程的比较原理研究了系统的全局渐近性质,获得了系统持续生存的一组充分条件．     

The geometrical analysis of a predator-prey model with two state impulses

Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results.     

A simple integrative electrophysiological model of bursting GnRH neurons

In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.     

带扩散的Barbour血吸虫病模型的定性分析(英文)

这篇文章主要考虑由常微分方程组和偏微分方程组构成的Barbour血吸虫病模型.偏微分系统是反映空间和时间分布的反应扩散系统.对模型的定性性质进行了分析.利用比较原理得出解的一致有上界性.同时利用能量方法证明出椭圆系统在扩散系数的一定范围内没有非常数的正稳态解.     

具收获与脉冲的时滞捕食模型研究

研究了与生物资源管理相关的食饵具脉冲扰动与成年捕食者具连续收获的阶段结构时滞捕食-食饵模型.利用离散动力系统的频闪映射和脉冲时滞微分方程理论,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.结论为现实的可再生生物资源管理提供了可靠的策略依据.     

Mathematical modelling of tissue-engineered angiogenesis

We present a mathematical model for the vascularisation of a porous scaffold following implantation in vivo. The model is given as a set of coupled non-linear ordinary differential equations (ODEs) which describe the evolution in time of the amounts of the different tissue constituents inside the scaffold. Bifurcation analyses reveal how the extent of scaffold vascularisation changes as a function of the parameter values. For example, it is shown how the loss of seeded cells arising from slow infiltration of vascular tissue can be overcome using a prevascularisation strategy consisting of seeding the scaffold with vascular cells. Using certain assumptions it is shown how the system can be simplified to one which is partially tractable and for which some analysis is given. Limited comparison is also given of the model solutions with experimental data from the chick chorioallantoic membrane (CAM) assay.     

Dynamics and stability of a three-dimensional model of cell signal transduction

In this paper, we consider a three-dimensional model of cell signal transduction. In this model, the deactivation of signalling proteins occur throughout the cytosol and activation is localized to specific sites in the cell. We use matched asymptotic expansions to construct the dynamic solutions of signalling protein concentrations. The result of the asymptotic analysis is a system of ordinary differential equations. This reduced system is compared to numerical simulations of the full three-dimensional system. As well, we consider the stability of equilibrium solutions. We find that the systems under consideration may undergo sustained oscillations, hysteresis and other complex behaviors. The simulations of the full three-dimensional system agree with simulations of the reduced ordinary differential equations.     

On Comparison of Series and Numerical Solutions for Flow of Eyring-Powell Fluid with Newtonian Heating And Internal Heat Generation/Absorption

In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both series and numerical solutions. Series solution is constructed using homotopy analysis method (HAM) whereas numerical solution is presented by two different techniques namely shooting method and bvp4c. A comparison of homotopy solution with numerical solution is also tabulated. Both solutions are found in an excellent agreement. Dimensionless velocity and temperature profiles are plotted and discussed for various emerging physical parameters.     

Kinetic modeling and fitting software for interconnected reaction schemes: VisKin

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.