PERSISTENCE AND GLOBAL STABILITY FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS

A three-species ratio-dependent predator-prey diffusion model with time de-lays is investigated. It is shown that the system is uniformly persistent under some ap-propriate conditions, and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.     

带时滞的比率型的食物链系统的持久性和稳定性

A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.     

PERMANENCE AND PERIODIC SOLUTION FOR NONAUTONOMOUS COMPETITION-PREDATOR SYSTEM WITH TYPE II FUNCTIONAL RESPONSE

A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.     

EFFECT OF TOXIC SUBSTANCE ON A NONAUTONOMOUS COMPETITIVE SYSTEM

In this paper, we consider a nonautonomous competitive system which is also affected by toxic substances. Some averaged conditions for the permanence of this system are obtained. Our result shows that under some suitable assumption on the coefficients of the system, the toxic has no influence on the permanence of the system. Also, by using a suitable Lyapunov function, sufficient conditions which guarantee the attractivity of any two positive solutions of the system are obtained.     

Generalized isochronous centers for complex systems

In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.     

APPROXIMATE CONTROLLABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.     

具线性退化特征场对角型方程组Goursat问题的奇性形成机制

For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.     

EXISTENCE OF POSITIVE SOLUTION TO A p-LAPLACIAN SYSTEM

A p-Laplacian system with Dirichlet boundary conditions is investigated. By the fibering method introduced by Pohozaev,we discuss the existence of positive weak solutions to the system under some proper conditions.     

A fast algorithm for multivariate Hermite interpolation

Multivariate Hermite interpolation is widely applied in many fields, such as finite element construction, inverse engineering, CAD etc.. For arbitrarily given Hermite interpolation conditions, the typical method is to compute the vanishing ideal I （the set of polynomials satisfying all the homogeneous interpolation conditions are zero） and then use a complete residue system modulo I as the interpolation basis. Thus the interpolation problem can be converted into solving a linear equation system. A generic algorithm was presented in [18], which is a generalization of BM algorithm [22] and the complexity is O（τ^3） where r represents the number of the interpolation conditions. In this paper we derive a method to obtain the residue system directly from the relative position of the points and the corresponding derivative conditions （presented by lower sets） and then use fast GEPP to solve the linear system with O（（τ ＋ 3）τ^2） operations, where τ is the displacement-rank of the coefficient matrix. In the best case τ = 1 and in the worst case τ = [τ/n], where n is the number of variables.     

Charpit System of Partial Differential Equations with Algebraic Constraints

In this paper the Charpit system of partial differential equations with algebraic constraints is considered. So, first the compatibility conditions of a system of algebraic equations and also of the Charpit system of partial differential equations are separately considered. For the combined system of equations of both types sufficient conditions for the existence of a solution are found. They lead to an algorithm for reducing the combined system to a Charpit system of partial differential equations of dimension less than the initial system and without algebraic constraints. Moreover, it is proved that this system identically satisfies the compatibility conditions if so does the initial system.     

具有反馈控制和功能反应的两种群竞争系统的解的渐近性

讨论了具有反馈控制和功能反应的两种群竞争系统的解的渐近性质,获得了在一定条件下该种群持续生存的充分条件,以及该系统为周期系统时,存在全局渐近稳定的正周期解。     

Persistence and Global Stability in a Delayed Gause-Type Predator-Prey System without Dominating Instantaneous Negative Feedbacks

A delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system.     

关于求解弹性力学平面问题的功的互等定理法

本文推广功的互等定理法于求解具有复杂边界条件矩形板的弹性力学平面问题.首先,我们给出了作为基本系统的四边固定矩形板平面问题的基本解,然后基于在具有复杂边界条件的实际系统与基本系统之间应用功的互等定理,从而求得实际系统的位移表达式.当只存在位移边界条件时,用功的互等定理法求得的位移表达式就是真实的.但是在另一些情况下,当有静力边界条件或混合边界条件时,所求得的位移是容许的.为求得真实位移.必须应用最小势能原理.一些计算表明.对于求解具有复杂边界条件的矩形板弹性力学平面问题,功的互等定理法是一简便通用的方法.显然,这是一个新方法.     

具有连续时滞和基于比率的非自治捕食扩散系统的持续生存

研究具有连续时滞和基于比率的非自治捕食扩散系统.证明了该系统一致持久性及任何正解全局渐近稳定性的充分条件.     

具有三个成长阶段的单种群时滞模型的永久持续生存和全局稳定性

该文研究具有分布时滞和三个成长阶段的单种群模型,得到了系统永久持续生存的充分条件;同时通过构造Lyapunov 函数得到了系统全局渐近稳定的充分条件;最后建立具体模型说明所得结果的可行性.     

二次多项式微分系统的反射函数

本文给出了二次多项式微分系统的反射函数的第一分量不依赖第二分量的充要条件，以及此时第二分量的表示式，及该系统存在周期解的条件。     

Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay

A two-species ratio-dependent predator-prey model with distributed time delay is investigated. It is shown that the system is persistent under some appropriate conditions, and sufficient conditions are obtained for both the local and global stability of the positive equilibrium of the system.