基于IPM策略和食物助增捕食者的捕食系统

研究了综合害虫治理(IPM)策略下具有脉冲作用和食物助增捕食者种群的捕食系统.得到了害虫灭绝周期解全局渐近稳定和系统持续生存的条件.     

食饵为Smith增长且具有合作狩猎的捕食模型动力学分析

建立了一类食饵种群为Smith增长并且考虑捕食者合作狩猎的捕食与被捕食模型,通过研究发现捕食者合作狩猎强度和食饵的净增长率会影响种群的共存状态.并且给出系统存在一个或多个共存平衡点的条件,当出现两个共存平衡点时,系统会呈现双稳状态,即种群或者保持稳定共存,或者捕食种群灭绝,食饵种群达到饱和;并且系统会在某些平衡点处发生Hopf分支,产生持续捕食者-食饵振荡;当两个共存平衡点重合时,系统会发生BT分支,呈现单稳状态,捕食者灭绝平衡成为惟一稳定状态.同时进行了相应的数值模拟和生物解释.     

具有Size结构的捕食种群系统的最优收获策略

分析了一类捕食者种群带有Size结构的捕食-被捕食系统的最优收获问题. 利用不动点定理证明了状态系统及其共轭系统非负解的存在唯一性、解对控制变量的连续依赖性. 应用切锥法锥技巧导出了最优性条件, 借助Ekeland变分原理讨论了最优收获策略的存在唯一性, 推广了年龄结构种群模型中的相应结论.     

食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型

本文讨论了与生物资源管理相关的食饵具脉冲扰动与捕食者具连续收获的时滞捕食-食饵模型,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件.也证明了系统的所有解的一致完全有界.我们的结论为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲时滞微分方程的理论.     

一类非二次微分食饵—捕食系统的脉冲控制

利用脉冲微分方程的比较原理对一个具有功能反应函数为x~(1/2)的食饵—捕食生物模型进行研究.考虑到模型存在的不确定性,研究了捕食者的捕食率不但受食饵的密度大小影响,同时还受捕食者本身的密度影响的生物系统.通过脉冲控制得到了使其渐近稳定到原先不稳定的正平衡点的充分条件,使食饵密度和捕食者密度保持在一个定数附近并给出了生态解释.     

利用最简几何不等式求最值

几个基本几何不等式如下 :(1)两点间距离最短 ;(2 )三角形两边之和大于第三边 ,两边之差小于第三边 ;(3)点到直线的距离最短 .把这几个基本几何不等式运用到数学中的一些最值问题中 ,将使整个解题过程令人耳目一新 .例 1　如图 1,若 A(3,2 ) ,F为抛物线y2 =2 x的焦点 ,P为抛物线上任意一点 ,求 :| PF| | PA|的最小值 ,以及取得最小值时 P的坐标 .解　由条件可知 ,抛物线的准线 l的方程为 x=- 1.设动点 P(x,y)在准线上的垂足为M(- 1,y) .∵　　 | PF| =| PM| ,∴　要求 | PF| | PA|的最小值 ,即是求 | PM| | PA|的最小值 .如…     

“设且求”寻求一类解析几何题求解新途径

1 困惑 2012年江苏高考第19题: 如图1,在平面直角坐标系xOy中,椭圆x2/a2+y2/b2=1(a＞b＞0)的左、右焦点分别为F1(-c,0),F2(c,0).已知点(1,e)和e,√3/2)都在椭圆上,其中e为椭圆的离心率. (1)求椭圆的方程; (2)设A,B是椭圆上位于x轴上方的两点,且直线AF1与直线BF2平行,AF2与BF1交于点P.     

一道高考题的几种求解策略

问题 给定抛物线C:y2=4x,F是C的焦 点,过点F的直线l与C相交于A、B两点,设 FB=λAF,若λ∈[4,9],求l在y轴上截距的 变化范围. 本题是2004年全国高考(理)数学(必修+ 选修Ⅱ)第21题的第二问. 本题难度并不是很大,考生之所以不能很 好地解决,主要是因为不能很好地对问题实施 转化.下面我们来看本题的几种解决策略.     

一道高考试题的推广

题目 (2009年辽宁文22)已知,椭圆C经过点A(1,(3)/(2)),两个焦点为(-1,0),(1,0). (1)求椭圆C的方程; (2)E,F是椭圆C上的两个动点,如果直线AE的斜率与AF的斜率互为相反数,证明直线EF的斜率为定值,并求出这个定值.     

直线与椭圆、双曲线位置关系的一种新的判定方法

我们知道 ,针对圆的特殊几何性质 ,可以用圆心到直线的距离与圆的半径的大小关系来判定直线和圆的位置关系 .实际上 ,结合椭圆和双曲线的第一定义 ,直线和椭圆、双曲线的位置关系的判定也有类似的结论 .引理 1　平面上 ,两点 F1 、F2 在直线 l的同侧 ,点 F′1 和点 F1 关于直线 l成轴对称 ,点 P在直线 l上 ,则 | PF1 | + | PF2 |≥ | F′1 F2 | (如图 1) .(证明略 )图 1　　　　图 2定理 1　直线上一点到椭圆两焦点的距离的和的最小值( 1)小于长轴长 ,则直线与椭圆相交 ;( 2 )等于长轴长 ,则直线与椭圆相切 ;( 3 )大于长轴长 ,则直线与…     

蜘蛛网结构性能研究

以蛛网捕丝与放射丝结点为研究对象,首先应用达朗贝尔原理对结点进行受力分析,运用动力松弛法将猎物作用于结点的动态力变为静力建模;然后考虑不同捕食策略对蛛网结构的影响,将捕食策略变为约束条件,蛛丝上的最小残余力作为优化目标,建立基于捕食策略的单目标规划模型;最后提出将环境影响因子转化为目标函数的约束条件的模型改进方法。     

Investigating the Turing Conditions for Diffusion-driven Instability in Predator-prey System with Hunting Cooperation Functional Response

In this paper, we focus on stability analysis of steady-state solutions of a predator-prey system with hunting cooperation functional response. The results show that the Turing instability can be affected not only the existence of hunting cooperation, but also the diffusion coefficients: (1) in the absence of predator diffusion, diffusion-driven instability can be induced by hunting cooperation, but no stable patterns appear; (2) the system can occur diffusion-driven instability and Turing patterns, when both predator and prey have diffusion, and the diffusion coefficient of prey is greater than that of the predator. The numerical simulations of two cases are presented to verify the validity of our theoretical results.     

Positive periodic solutions for Lotka–Volterra systems with a general attack rate

The paper deals with a non-autonomous Lotka–Volterra type system, which in particular may include logistic growth of the prey population and hunting cooperation between predators. We focus on the existence of positive periodic solutions by using an operator approach based on the Krasnosel’skii homotopy expansion theorem. We give sufficient conditions in order that the localized periodic solution does not reduce to a steady state. Particularly, two typical expressions for the functional response of predators are discussed.     

Stability and global Hopf bifurcation in a delayed food web consisting of a prey and two predators

This paper is concerned with a predator–prey system with Holling II functional response and hunting delay and gestation. By regarding the sum of delays as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. We obtained explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation. Using a global Hopf bifurcation result of Wu [Wu JH. Symmetric functional differential equations and neural networks with memory, Trans Amer Math Soc 1998;350:4799–4838] for functional differential equations, we may show the global existence of the periodic solutions. Finally, several numerical simulations illustrating the theoretical analysis are also given.     

ON THE MANAGEMENT OF INTERCONNECTED WILDLIFE POPULATIONS

Abstract Economic interdependency of wildlife or fish stocks is usually attributed to ecological interdependency, such as predator–prey and competitive relationships, or to density‐dependent migration of species between different areas. This paper provides another channel for economic interdependency of wildlife where density‐independent migration and market price interaction affect the management strategies among different landowners. Management is studied under three market conditions for selling hunting licenses: price taking behavior, monopoly market, and duopoly market. Harvesting of the Scandinavian moose is used as an example. The paper provides several results on how economic interdependency works through the migration pattern. When a duopoly market is introduced, hunting license price interaction among the landowners plays an additional role in determining the optimal harvesting strategy.     

网球发球的最佳策略

本文为网球运动员提供了如何选择快发球和慢发球的策略来提高赢球的概率 .通过用决策树表示F F,F S,SF,SS几种不同的策略 ,根据最大概率和最大期望值准则提出了概率意义下的最佳策略 ,考虑到网球运动的特点 ,为赢得全盘的胜利又制订了 BT策略 .最后 ,通过计算机模拟对两种策略进行了比较 .     

Analysis of a predator–prey model with Holling II functional response concerning impulsive control strategy

According to biological and chemical control strategy for pest control, we investigate the dynamic behavior of a Holling II functional response predator–prey system concerning impulsive control strategy-periodic releasing natural enemies and spraying pesticide at different fixed times. By using Floquet theorem and small amplitude perturbation method, we prove that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, the condition for the permanence of the system is also given. Numerical results show that the system we consider can take on various kinds of periodic fluctuations and several types of attractor coexistence and is dominated by periodic, quasiperiodic and chaotic solutions, which implies that the presence of pulses makes the dynamic behavior more complex. Finally, we conclude that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently.     

Hopf bifurcations in a predator–prey system with a discrete delay and a distributed delay

A delayed Lotka–Volterra two-species predator–prey system with discrete hunting delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. It is found that under suitable conditions on the parameters the positive equilibrium is asymptotically stable when the hunting delay is less than a certain critical value and unstable when the hunting delay is greater than this critical value. Meanwhile, according to the Hopf bifurcation theorem for functional differential equations (FDEs), we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the hunting delay crosses through a sequence of critical values. In particular, by applying the normal form theory and the center manifold reduction for FDEs, an explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions occurring through Hopf bifurcations is given. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.     

常数比例投资组合保险(CPPI)策略 --捐赠型基金投资策略的最优选择

本文采用Merton提出的处理捐赠型基金的连续时间模型的一般框架，分析了在风险资产为几何布朗运动，效用函数为CRRA效用函数，且捐赠型基金有动态最低支出时的最优支出策略和最优投资策略，结果表明存在一条策略基准线，当基金的总资产在策略基准线之上时，基金管理人关于基金支出与投资策略的选择与不存在最低支出的要求时所作出的决策是一样的，但是一旦基金的总资产低于这条策略基准线时，基金管理人便需要考虑到基金将来必要的支出，并实际影响到他对投资策略的选择，此时基金管理人可作的最优选择是：最低的支出和一种为复制幂收益函数期权的CPPI投资策略。     

On a stoichiometric two predators on one prey discrete model

In this letter, we first propose a discrete analogue of a continuous time predator–prey system, which models the dynamics of two predators on one prey [I. Loladze, Y. Kuang, J. Elser, W.F. Fagan, Competition and stoichiometry: Coexistence of two predators on one prey, Theor. Popul. Biol. 65 (2004) 1–15]. Then, we study the dynamics of this discrete model. We establish results on boundedness and global attractivity. Finally, several numerical simulations are given to support the theoretical results.