Global asymptotic stability of a two species competitive system with stage structure and harvesting

Introduction' There have recently appeared in the literature several mathematical models of stagestructured population growth, i. e., models which take into account the faCt that individuals in a population may belong to one of two classes, the immatures and the matureslllZI.Cannibalism has been observed in a great variety of species, including a number of fish species.Cannibalism models of various types have also been investigatedI3"l. In these models, the ageto maturity is represented by a…     

The effect of diffusion on the permanence of Smith population model in a polluted patch

IntroductionThe effect of diffusion on the permanence of population has been studied in some refer-ences. LevinI1] set up the followiIlg model to study the effect of diffusion on the permanence ofpopulation:: f \' \ =.tvhere ur(t) defines the number of population i in patch p, uu = (ut,'. u:). f,u(uu) isthe int!.i11sic growth rate fOr population t, and D:' is the (1iffosive rate of population l frompatch 7 to patch U. Hastingsi2J proved that the positive equilibrium state is stab1e for suf…     

具有年龄结构的种群线性动力系统的最优收获控制问题

§ 1　Introduction and setting of the problemThe optimal control of age-dependent population dynamics has been intensivelystudied in the last two decades and there is now a vast stock of literature on the topic ofoptimal control problems ofage-structured population dynamics.(see [1 -9] ) .To the bestof our knowledge,the works of Brokate[3,4] are the firstto deal with this topic.Since then,many authors devote to the optimal harvesting problem.In this aspect,we refere to thefundamental papers o…     

具有阶段结构和时滞的捕食系统

§ 1　IntroductionThe competitive,cooperative and predator-prey models have been studied by many au-thors.[1— 4] The permanence (or strong persistence) and extinction are significant conceptsof those models.However,the stage structure of species has been considered very little.Inthe real world,almost all animals have the stage structure of immature and mature.Re-cently,papers[5— 7] studied the stage structure of species,the transformation rate of ma-ture population is proportional to the ex…     

GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS

The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.     

EXISTENCE OF OPTIMAL FERTILITY RATE IN POPULATION CONTROL PROBLEM

The population growth and control are an important problem for mankind. In the paper [13], the critical fertility rateβ_cr in the population problem has been investigated and the relation between fertility rateβ and population growth has been given. It is natural     

Populations with individual variation in dispersal in heterogeneous environments: Dynamics and competition with simply diffusing populations

We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reactiondiffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".     

A skew–normal mixture of joint location,scale and skewness models

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models: a skew–normal mixture of joint location,scale and skewness models to analyze the heteroscedastic skew–normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation–Maximization(EM) algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index(BMI) data are presented.     

Optimal Harvesting and Stability for a Predator-prey System with Stage Structure

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.     

SPECTRAL PROPERTIES OF POPULATION OPERATOR AND ASYMTOTIC BEHAVIOUR OF POPULATION SEMIGROUP

In this paper we discuss the spectral properties of the Population operator, prove that the population operator has only one real eigenvalue γ_0, which is greater that real parts of other eigenvalues,and find the corresponding relation between γ_0 and the critical fertility rate β_(cr). We also study the existence and asymptotic behaviour of the semigroup for the population system, then come to the conclusion about the stability of the population system,including the existene of the steaby population state in the critical case of the fertility rate.These are all the new results of the quantitative population theory.     

PERIODIC AND ALMOST PERIODIC SOLUTIONS OF A CERTAIN INFINITE DELAY INTEGRAL EQUATION

In this paper,by using successive approximation method and fixed-point theorem,we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the peri- odic and almost periodic solutions of the system.     

PERIODIC SOLUTIONS AND STABILITY ANALYSIS FOR NEURAL NETWORKS WITH TIME-VARYING DELAY

1 IntroductionIt is well known that both in biological and man-made neural systems, inte-gl.ation afld communication delays are ubiquitous, and often become sources ofinstabilitY' The de1ays in electronic neural networks are usually time varying,and sometimes vary vio1ently with time due to the finite switching speed ofamplifiers and faults in the electrical circuit. They s1ow down the transmissionrate and tend to introduce some degree of instability in circuits. Therefore,fast response must …     

时滞Lotka-Volterra系统的持久性和周期解

本文研究具有时滞周期捕食系统的持久性和周期解,得到了系统永久持续生存的充要条件。在此条件下系统存在正的ω周期解,改进了一些已知结果。     

一类平面非线性系统无闭轨的充分条件

本文建立了一类平面非线性系统无闭轨的若干充分条件．     

Minimal sets in monotone and sublinear skew-product semiflows I: The general case

The dynamics of a general monotone and sublinear skew-product semiflow is analyzed, paying special attention to the long-term behavior of the strongly positive semiorbits and to the minimal sets. Four possibilities arise depending on the existence or absence of strongly positive minimal sets and bounded semiorbits, as well as on the coexistence or not of bounded and unbounded strongly positive semiorbits. Previous results are unified and extended, and scenarios which are impossible in the autonomous or periodic cases are described.     

线性时变切换系统的渐近稳定性研究

考虑一类线性时变切换系统的渐近稳定性.基于矩阵测试理论,文中给出线性时变切换系统在周期切换和等时切换下渐近稳定的充分条件,并通过仿真实例说明结论是正确的.     

OSCILLATION AND EXISTENCE OF POSITIVESOLUTIONS OF DIFFERENTIAL EQUATIONSWITH POSITIVE, NEGATIVE COEFFICIENTS

This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The "sharp" conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.     

拟弱几乎周期点的等价定义与系统的混沌性

1992年, 周作领引进了弱几乎周期点这一概念. 1995年, 周和何伟弘又引进了拟弱几乎周期点这个概念, 并利用它们深刻地刻画了一个动力系统的本质所在. 为了更好地看出这两者的区别,首先从回复时间集的角度给出拟弱几乎周期点的等价定义,然后研究了一个存在真的拟弱几乎周期点的系统的混沌情况,得到了这样的系统是Takens-Ruelle混沌的.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.     

一类奇异边值问题正解存在的充分必要条件

研究一类奇异边值问题解的存在性及解的迭代,得到C[0,1]正解和C1[0,1]正解存在的充分必要条件,从本质上改进和推广了赵增勤1998年的工作．