THE OPTIMAL HARVESTING OF A PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE

In this paper,we establish the exploitation of continuous harvest of preda- tor and prey with stage-structures.We investigate the properties of harvesting multispecies systems.With some special methods,we obtain boundedness and global attractiveness of all the nonnegative equilibria for proportional harvest. Finally,we solve the problem of optimal harvest policy using Pontragin's ma- ximal principle.     

非自治的具有阶段结构和时滞的捕食系统的动力学行为

本文研究了一个非自治的具有阶段结构和时滞的捕食-食饵模型.利用比较原理获得了系统持久性的条件,在假设系统为周期系统的条件下通过构造Liapunov函数证明了正周期解的存在唯一性和全局渐近稳定性.     

关于捕食者种群具有阶段结构和疾病的捕食-被捕食模型(英文)

本文研究了捕食者种群具有阶段结构和疾病的捕食-被捕食模型.利用比较定理、分析特征方程和迭代的技巧,得到了模型永久持续生存和模型的非负平衡位置稳定的充分性条件.通过对结果的分析我们可以给出疾病的基本再生数,这对疾病的防治有很大的意义.     

具有饱和与竞争项的捕食系统的全局分歧及稳定性

利用比较原理,分歧理论,特征值线性扰动理论,主要研究了一类具有饱和与竞争反应项的捕食-食饵系统在Dirichlet边界条件下的平衡态分歧解.首先给出了一个先验估计和局部分歧解存在的充分条件.然后对局部分歧解进行了全局延拓,得到了该系统平衡态的全局分歧解及其走向.最后讨论了局部分歧解的稳定性.     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

随机配对的食饵-捕食者模型

建立了食饵具有性别结构的食饵-捕食者模型,其中食饵两性的配对是随机的.结论表明:没有偏食的捕食不能改变食饵的性比,偏食可以改变食饵的性比;若食饵两性的出生率相等,任意的偏食都可以消除周期振荡;若食饵两性的出生率不相等,较大的偏食总能消除周期振荡,周期振荡的消除与否由偏食系数和食饵两性的出生率之比共同决定.     

具交叉感染的流行病模型的数学分析

In this paper,an initial boundary value problem with homogeneous Neumann boundary condition is studied for a reaction-diffusion system which models the spread of infectious diseases within two population groups by means of self and criss-cross infection mechanism. Existence,uniqueness and boundedness of the nonnegative global solution (u1,u2,u3,u4),existence of the limit of the solution as t→+∞,namely,(u1,u2,u3,u4)→(u*1,0,u*3,0),are proved.     

IMPULSIVE VACCINATION OF SIRS EPIDEMIC MODEL WITH STAGE-STRUCTURE

The period of infection is partitioned into the early and later stages according to the development process of infection. The infected individuals in the different stages have the different ability of transmitting disease. The constant recruitment rate and exponential natural death, as well as the disease-related death and pulse vaccination are incorporated into the model. Through the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the sy...     

具有饱和的Prey—Predator模型的长时间行为

本文研究了具有饱和的Ｐｒｅｙ－Ｐｒｅｄａｔｏｒ模的长时间为。     

ATTRACTING BEHAVIOR OF INSHORE-OFFSHORE FISHING MODEL WITH STAGE-STRUCTURE

This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of differential equations, steady states of this dynamical systems representing fishery are derived, and their globally attracting behaviors are discussed. A brief biological meaning for the mathematical results is given.     

Razumikhin Type Theorems on Boundedness

ＲａｚｕｍｉｋｈｉｎＴｙｐｅＴｈｅｏｒｅｍｓｏｎＢｏｕｎｄｅｄｎｅｓｓＺｈａｎｇＳｈｕｎｉａｎ（张书年）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２００２４...     

一类多分子反应模型的Hopf分歧解

本文用Ｌｉａｐｕｎｏｖ函数和Ｈｏｐｆ分歧定理讨论一类多分子反应模型ｄｘ／ｄｔ＝δ－ａｘ－ｘ＾ｐｙ＾ｑ，ｄｙ／ｄｔ＝ｘ＾ｐｙ＾ｑ－ｂｙ对ａ＝０，ｐ＝２，ｑ≥２，得到Ｈｏｐｆ分歧解的存在性，唯一性，稳定性及分歧解的渐近表达式。     

ASYMPTOTIC PROPERTY FOR A LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH DELAYS AND DISPERSION

An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution.     

COEXISTENCE STATES OF A STRONGLY COUPLED PREY-PREDATOR MODEL

This paper is concerned with a strongly coupled prey-predator model with homogeneous Dirichlet boundary conditions. The existence and uniqueness of coexistence states are discussed.     

PERIODIC SOLUTION AND ALMOST PERIODIC SOLUTION OF NONAUTONOMOUS COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING

In this paper, a two-species nonautonomous competitive model with stage structure and harvesting is considered. Sufficient conditions for the existence, uniqueness, global attractivity of positive periodic solution and the existence, uniform asymptotic stability of almost periodic solution are obtained.     

一类具有阶段结构的捕食-食饵种群收获模型

本文研究了一类具有阶段结构和密度制约的捕食-食饵两种群同时收获模型.利用比较定理,Barbalt引理,极人值原理等,获得了平衡点稳定性的充分条件,以及在不同情况下,各种群以最大可持续收获量为管理目标的最优生存量和最大收获量.     

Qualitative properties of solutions of integral equations

In this paper we study a linear integral equation in which the kernel fails to satisfy standard conditions yielding qualitative properties of solutions. Thus, we begin by following the standard idea of differentiation to obtain . The investigation frequently depends on x^′(t)+C(t,t)x(t)=0 being uniformly asymptotically stable. When that property fails to hold, the investigator must turn to ad hoc methods. We show that there is a way out of this dilemma. We note that if C(t,t) is bounded, then for k>0 the equation resulting from x^′+kx will have a uniformly asymptotically stable ODE part and the remainder can often be shown to be a harmless perturbation. The study is also continued to the pair x^″+kx^′.     

A LOTKA-VOLTERRA PREY-PREDATOR SYSTEM WITH FEEDBACK CONTROL EFFECT

In this paper, we propose a Lotka-Volterra prey-predator system with discrete delays and feedback control. Firstly, we show that solution of the system is bounded. Secondly, we obtain sufficient condition for the global stability of the unique positive equilibrium to the system.     

一类分两段收取保费的相关风险模型

本文研究了一类索赔时间间隔与索赔量相关且分两段收取保费的风险模型.利用微分的方法得到了罚金折现期望满足的积分-微分方程,并给出了此方程解的一个表达式.