非线性中立双曲型脉冲偏微分方程解的振动性质

讨论一类非线性中立双曲型脉冲偏微分方程解的振动性质,应用积分不等式,在第二类边界条件下获得了其一切解振动的充分条件.     

基于脉冲和时滞影响的非线性双曲型方程的振动准则

研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏微分方程的振动性,利用特征函数法和一阶脉冲时滞微分不等式,获得了该类方程在Robin边值条件下所有解振动的若干充分性判据,所得结果推广和包含了最新文献中的结果.     

具偏差变元的偏微分方程组的振动性定理

获得了一类具偏差变元的偶数阶偏微分方程组解振动的若干充分条件。     

分数阶偏微分方程解的强迫振动性质（英文）

讨论了一类分数阶时滞偏微分方程解的强迫振动性质,应用微分不等式与黎曼-刘维尔定义下的分数阶微分性质,在罗宾边界条件下获得了其一切解振动的充分条件,并举例论证了相关结论.     

高阶非线性中立型偏微分方程解的振动性

考虑一类高阶非线性中立型偏微分方程,获得了方程的所有解振动的充分条件,同时也给出了实际应用例子。     

具有强迫项的二阶中立型微分方程的振动准则

利用广义的黎卡提变换对具有强迫项的二阶中立型微分方程的振动性进行了研究,获得了该类方程存在振动解的充分条件.探讨了一类微分方程中的强迫项在方程存在振动解性质中的内在联系,改进和推广了已有文献的结果,并给出了应用实例.     

一种非线性泛函微分方程振动性

讨论一类二阶非线性泛函微分方程的解的振动性质,建立了方程的振动性定理,在一定条件下,建立了几个新的振动性定理.     

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.     

非线性高阶阻尼时滞微分方程的振动定理

研究具有阻尼项的非线性时滞微分方程,给出了使得方程的一切解振动的两个充分条件.一些实例说明,本文的结果在判定非线性阻尼方程的振动性时较文献中的结果更为有效.     

具有阻尼项广义Emden-Fowler时滞微分方程的振动性

运用广义Riccati变换和中值定理,讨论了具有阻尼项的广义Emden-Fowler时滞微分方程的振动性及渐近性质,就α与β的关系分四种情况,得到了该方程存在振动解的充分条件,推广和改进了已有结果,并用实例给出了其应用.     

Oscillations in a refractory neural net

A functional differential equation that arises from the classic theory of neural networks is considered. As the length of the absolute refractory period is varied, there is, as shown here, a super-critical Hopf bifurcation. As the ratio of the refractory period to the time constant of the network increases, a novel relaxation oscillation occurs. Some approximations are made and the period of this oscillation is computed.     

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。     

Zum Mechanismus der biologischen 24-Stunden-Periodik

Summary The level (=arithmetic average of all instantaneous values)of a self-sustained oscillation in general influences all properties of the oscillation, including period, amplitude and shape of the oscillation, and the rate of exchange of energy between the oscillator and its environment. Only when the non-linear damping factor does not depend on the instantaneous value of the oscillating function, but only on the amplitude of the oscillation, are the other properties independent of the average level. The differential equations describing self-sustained oscillations cannot be solved exactly, but methods of approximation are applicable. Numerical solutions to several different forms of the equations will be discussed.In the simplest case (van der Pol equation) all properties of the self-sustained oscillation (e.g. period, amplitude) are extreme when the level is zero. The oscillation continues only within a given range of levels (oscillating range); outside this range, the oscillation damps out. In other modifications of the equation, the oscillating function cannot assume a zero value. In all cases, the extent to which the average level influences the different properties depends on the factor , which describes the position of the oscillation within the range between harmonic and relaxation types of oscillation.In the elementary van der Pol equation, the correlation between level and frequency changes sign within the oscillating range; that is, the circadian rule, demanding an always positive correlation between level and frequency, cannot be fulfilled. Only with an additional non-linearity in the energy of recoil does the correlation remain unchanged in sign throughout the oscillating range. A stability condition demands a positive sign for this non-linearity, and hence, for the correlation (fulfilling the circadian rule); if the sign is negative (violating the circadian rule), the oscillation becomes unstable. With an additional term of the third order, the oscillation acquires a two-peaked shape typical of many circadian oscillations.A simple differential equation describing all general properties of the circadian periodicity must fulfil these conditions: the oscillation must be self-sustained and limited to positive values; and the energy of recoil must be non-linear with a positive coefficient to obtain the appropriate correlation between level and frequency. In the equations here developed the environment directly influences only one parameter of the oscillation, i.e. the level. In addition to the circadian periodicity, the differential equations here examined describe the behavior of several other biological oscillations.

---

---

Die benutzten mathematischen Begriffe folgen — soweit dort angeführt — den Benennungen des DIN-Blattes 1311; im Anhang I sind die wichtigsten Begriffe noch einmal zusammenfassend definiert.     

Global positive coexistence of a nonlinear elliptic biological interacting model

The purpose of this note is to give a necessary and sufficient condition for the coexistence of positive solutions to a rather general type of elliptic predator-prey system of the Dirichlet problem on the bounded domain omega when omega is a subset of Rn is large. The result is that the partial differential equation system possesses positive coexistence if and only if the corresponding ordinary differential equation system has positive equilibrium, the positive constant states. This result thus yields an algebraically computable criterion for the positive coexistence of predator and prey in many biological models.     

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.     

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。     

高阶线性泛函方程解的振动性

考虑一类高阶线性泛函方程解的振动性,我们获得一些新的振动准则.这些振动准则,推广或改进了一些文献中的某些结果.     

Undamped oscillations in prey–predator models on a finite size lattice

Sustained oscillation is frequently observed in population dynamics of biospecies. The oscillation comes not only from deterministic but also from stochastic characteristics. In the present article, we deal with a finite size lattice which contains prey and predator. The interaction between a pair of lattice points is carried out by two different methods; local and global interactions. In the former, interaction occurs between adjacent sites, while in the latter interaction takes place between any pair of lattice sites. It is found that both systems exhibit undamped oscillations. The amplitude of oscillation decreases with the increase of the total lattice sites. In the case of global interaction, we can present a stochastic differential equation which is composed of two factors, i.e., the Lotka–Volterra equation with density dependence and noise term. The quantitative agreement between theory and simulation results of global interaction is almost perfect. The stochastic theory qualitatively expresses characteristics of sustainable oscillation for local interaction.     

Oscillation frequencies of tapered plant stems

Free oscillations of upright plant stems, or in technical terms, slender tapered rods with one end free, can be described by considering the equilibrium between bending moments in the form of a differential equation with appropriate boundary conditions. For stems with apical loads, where the mass of the stem is negligible, Mathematica 4.0 returns solutions for tapering modes α = 0, 0.5, and 1. For other values of α, including cases where the modulus of elasticity varies over the length of the stem, approximations leading to an upper and a lower estimate of the frequency of oscillation can be derived. For the limiting case of ω = 0, the differential equation is identical with Greenhill's equation for the stability against Euler buckling of a top-loaded slender pole. For stems without top loads, Mathematica 4.0 returns solutions only for two limiting cases, zero gravity (realized approximately for oscillations in a horizontal orientation of the stem) and for ω = 0 (Greenhill's equation). Approximations can be derived for all other cases. As an example, the oscillation of an Arundo donax plant stem is described.