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…     

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.     

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".     

递增年金的双随机模型

The dual random models about the life insurance and social pension insurance have received considerable attention in the recent articles on actuarial theory and applications. This paper discusses a general kind of increasing annuity based on its force of interest accumulationfunction as a general random process. The dual random model of the present value of the benefits of the increasing annuity has been set, and their moments have been calculated under certainconditions.     

Positive Periodic Solutions of a Class of Non-autonomous Single Species Population Model with Delays and Feedback Control

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.     

EXISTENCE AND GLOBAL ATTRACTIVITY OF POSITIVE PERIODIC SOLUTION OF A LOGISTIC GROWTH SYSTEM WITH FEEDBACK CONTROL AND DEVIATING ARGUMENTS

1 IntroductionIn recent years5 the application of theories of functional differential equationsin mathematical ecology has been developed rapidIy. Various mathematicalmodels have been proposed in the study of population dynarnics, ecology andepidemic. Some of them are described as non-autonomous delay differentialequations. Many authors studied the dynamics of population with deIays whichis usefuI for the control of the population of the mankind, animals and theenvironment. One of the famous…     

Statistical inferences for varying-coefficint models based on locally weighted regression technique

1. IntroductionIn recent y6ars, some progress has been made towards increaJsing the flexibility of linearregression models. One of the obvious extensions in this direction is the sthcalled varyingcoefficient regression models in which the regressiOn funtions are llnear in the regressors,but their coefficients are allowed to change with the value of another factor. Specificallysuppose that we have a response variable Y and regressors X1 t X2,' t Xv as well as anothervariable V. A varyingco…     

THE C-K MODEL WITH SOLVABLE ENDOGENOUS FERTILITY

§ 1　 IntroductionThe relationship of population and economic growth is one of the most importantproblems in modern economic growth theory.Establishing a mathematical model theoreti-cal to study the interrelation of population and economic growth becomes a fundamentalmethod in this field[1～ 7] .In the papers[8,9] ,we obtain the especial C-K models with solv-able endogenous fertility under the specified strongly additive utility function and Cobb-Douglas production function.In the models,th…     

THE COLLOCATION METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS

1 Introduction Singular integral equations (SIEs) with Cauchy kernels Of the formoften arise in mathematical models of physical phenomena. Since closed-form solutions to SIEsare generally not available, much att.ntion has been focused on numerical methods of solution.In the past twenty years, various collocation methods for SIEs have been the topic of a greatmany of papers, most of which can be found in two surveys[213]. The early works in the fieldis to study tile numerical solutions for…     

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.     

A PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND HARVESTING FOR PREDATOR

In this paper, we consider a predator-prey system with stage structure and harvesting (where the predator population has two stages, an immature stage and a mature stage with harvesting, and the growth of the prey population is of Lotka-Volterra nature). We obtain the conditions of the globally asymptotic stability for three nonne-gative equilibria of this system.     

基于年龄结构的种群系统的最优收获控制

研究一类带年龄结构的非线性种群系统的最优收获问题.建立单种群阶段结构模型,对成年、幼年种群同时捕获,得到了单种群阶段结构模型在正平衡点渐近稳定的充分条件;并给出了脉冲控制时间间隔的上界估计值.分别对其幼年种群和成年种群捕获问题,给出以最大捕获可持续均衡收获(M SY)为目标的最优捕获策略.     

具有年龄结构的单种群模型的脉冲控制及其捕获策略

给出单种群阶段结构模型,利用脉冲微分方程的比较原理,通过状态反馈和输出反馈对模型变换后的系统进行了脉冲控制.对成年、幼年种群同时捕获,通过状态反馈,得到了单种群阶段结构模型在正平衡点渐近稳定的充分条件;通过输出反馈得到了相应的结论;并给出了脉冲控制时间间隔的上界估计值.分别对其幼年种群和成年种群捕获问题,给出以最大捕获可持续均衡收获(MSY)为目标的最优捕获策略.     

Global attractivity of nonautonomous stage-structured population models with dispersal and harvest

The nonautonomous stage-structured single-species dispersal model with harvesting of mature individuals in an N-patch environment is considered, in which the individual members of the population have a life history that takes them through two stages, immature and mature. By using the theory of monotone and concave operators to functional differential equations, we establish conditions under which this population dynamical system admits a positive periodic solution which attracts all positive solutions.     

Positive Periodic Solution and Numerical Optimization in the Harvesting Effort for a Single-Species Stage-Structured System with Birth Pulses

In this paper, we consider a single-species stage-structured model with birth pulses and the harvesting of the species. Especially, we assume that the species can be divided into the immature and the mature, which exhibit different death rates. The mature species reproduces at fixed moments each year because the birth of many species is seasonal or occurs in a regular pulse, and the species is harvested not during the whole year but during a single period of the year. For such a system, we obtain conditions which guarantee the existence of a stable positive periodic solution. This implies that sustainable exploitation of the species can be maintained if we use the proper strategy in the harvesting effort and timing. Further, in order to get the maximum annual sustainable yield, we optimize the harvesting using numerical analysis; in addition, we find that the harvesting timing affects the maximum annual sustainable yield. Lastly, we show the effects of birth rate and harvesting effort on the dynamical complexity of the system with the help of a bifurcation graph.     

Stable coexistence mediated by specialist harvesting in a two zooplankton–phytoplankton system

This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings.     

连续收获捕食者与脉冲存放食饵的阶段结构捕食-食饵模型的全局吸引和一致持久

研究了一个捕食者具连续收获与食饵具脉冲存放的阶段结构时滞捕食-食饵模型．根据生物资源管理的实际,改进了捕食者具阶段结构的捕食-食饵模型,即原来假设每个捕食者个体都具有相同的捕食食饵的能力．假设捕食者按年龄分为两个阶段,即幼体和成体,而且幼体无能力捕食食饵．得到了捕食者灭绝周期解全局吸引和系统持久的充分条件．结论说明了脉冲存放食饵对系统的持久起了重要的作用,并且为生物资源管理提供了策略基础．数值分析也进一步说明了系统的动力学性质．     

OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper,the impulsive exploitation of two species periodic competitive system is considered.First,we show that this type of system with impulsive har- vesting has a unique positive periodic solution,which is globally asymptotically stable.Further,by choosing the maximum total revenues as the management objective,we investigate the optimal harvesting policies for periodic competi- tive system with impulsive harvesting.Finally,we obtain the optimal time to harvest and optimal population level.     

Optimal pulse fishing policy in stage-structured models with birth pulses

In this paper, we propose exploited models with stage structure for the dynamics in a fish population for which periodic birth pulse and pulse fishing occur at different fixed time. Using the stroboscopic map, we obtain an exact cycle of system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or pulse fishing time or harvesting effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling, multi-period-halving and incomplete period-doubling bifurcation, pitch-fork and tangent bifurcation, non-unique dynamics (meaning that several attractors or attractor and chaos coexist) and attractor crisis. This suggests that birth pulse and pulse fishing provide a natural period or cyclicity that make the dynamical behaviors more complex. Moreover, we show that the pulse fishing has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. An interesting result is obtained that, after the birth pulse, the population can sustain much higher harvesting effort if the mature fish is removed as early as possible.