具常数投放率功能反应为／x的食饵-捕食系统的定性分析

本文研究一类具有常数投放率的食饵-捕食系统的定性行为,得到了正平衡点全局渐近稳定以及在正平衡点周围存在唯一极限环的充分条件．利用数值模拟检验了结论．     

一类捕食—食饵系统的定性分析

本文分析了一类具有Holling Ⅰ型功能性反应的捕食者种群与食饵种群相互作用的数学模型得出了如下结论:当e≥1,cd+br-ec~2x_0<0时,且b充分小则至少存在一个极限环;如果更要求d+r-ecx_0<0,b充分小时至少存在两个极限环。     

一类捕食-食饵系统的定性分析

本文用定性分析的方法研究了一类捕食-食饵系统的全局性质,给出了该系统不存在极限环以及存在唯一稳定极限环的条件．     

一类捕食者—食饵系统的稳定性

本文研究了具有一个公共食饵和两个互相竞争的捕食者系统，在扩散的影响下，平衡态的线性和非线性稳定性的变化情况。     

具有捕食正效应的捕食-食饵系统

在经典的捕食食饵系统中考虑到由于捕食效应对食饵种群带来的正向调节作用后,提出了具有捕食正效应的捕食-食饵系统.通过对模型的动力学行为的分析,从理论上说明了正向调节作用对系统的影响,并就第一象限内平衡点存在时的相图解释了捕食正效应的作用.结果表明:(1)捕食系统中适当的正向调节作用会增加系统的稳定性;(2)当捕食正效应达到一定的程度后系统拥有一个不稳定的极限环;(3)当捕食正效应过大时会使系统的稳定性发生变化,使捕食者种群与食饵种群同时趋向无穷,出现了调节放纵现象.这些结果在保护生物学中具有重要的意义.     

一类离散Leslic捕食-食饵系统的捕获策略

应用生物数学理论研究生态平衡与可持续发展是生态系统的一个热门课题.在海洋渔业的捕捞过程中,既要保证生态平衡,又要使捕捞收益最大更是海洋渔业关注的重要课题.目前对离散系统的捕捞研究较少.运用离散差分方程的稳定性理论,讨论一类具有捕获的离散Leslic捕食-食饵种群的系统,获取正平衡点的局部渐近稳定的充分条件.通过构造适当的Liapunov函数,利用二元函数的泰勒展开式讨论正平衡点存在必全局稳定性的结果.利用函数的极值判定法讨论在维持稳定捕获前提下的最优捕获策略,来获取最优经济效益.最后,通过一个适当的例子及数值模拟的说明主要结果是合理的.给实际生产提供了理论依据,具有一定的指导意义.     

一类食饵种群具有常数存放率的Kolmogorov系统的定性分析

本文对一类食饵种群具有常数存放率的Kolmogorov系统进行了定性分析,研究了系统平衡点的性态,证明了极限环的存在和唯一性．     

具有一般形式的脉冲捕食-食饵系统的持续生存性

研究了在周期环境中一大类脉冲捕食-食饵系统的持续生存性,数学模型由具有一般形式的周期脉冲微分方程描述.由脉冲微分方程比较定理和一些分析技巧,通过一系列命题和引理最终获得系统持续生存性结果的证明.由于所研究模型的一般性,得到的理论结果具有普遍的适用性,可为种群系统的生态平衡及可持续发展提供决策依据.     

一类食饵种群具有常数收获率的Kolmogolov系统的非线性分析

本文对一类食饵种群具有常数收获率的Ｋｏｌｍｏｇｏｌｏｖ系统进行了非线性分析,研究了 系统平衡点的性态,在较宽的条件下证明了系统不存在闭轨线;并获得了系统存在两个极限环的条件。     

一类食饵具有S-型变收获率的非自治离散捕食系统渐近行为

建立并研究了一类具有S-型变收获率的非自治离散捕食系统,应用差分不等式、Brouwer不动点定理和分析技巧分别建立了系统的持久生存性,正周期解的存在性及全局渐近稳定性的充分条件,我们还给出了具体验证例子及相应的数值模拟结果.     

一类具有非单调增长率和功能反应的捕食者-食饵系统的定性分析

考虑一类食饵密度具有非单调增长率,捕食者具有功能性反应的捕食者一食饵系统。得到系统在第一象限内正平衡点的区域稳定的条件和极限环存在唯一的条件,完整地讨论了系统(1)的拓扑结构。     

一类考虑收获的Monod-Haldane型捕食系统的动力学行为(英文)

给出了一类考虑收获的Monod-Haldane型捕食者-食饵系统的平衡点和稳定性分析,及给出几类分支的分析,包括鞍结分支、Bogdanov-Takens分支、超临界和亚临界Hopf分支,最后给出了数值模拟例子验证了结论的正确性.     

一类被开发的捕食系统的定性分析

讨论了一类食饵种群被开发的两种群捕食系统: dx/dt=x(a0+a1x-a2x2-a3y3)-h0, dy/dt=y(x-1)其中a0>0,a2>0,a3>0,h0>0,a1不定号.文中主要讨论了系统平衡点的行为以及系统的稳定性.用Pioncare切性曲线法及Dulac函数法讨论闭轨不存在的充分条件;用Hopf分支方法及张芷芬唯一性定理证明了极限环的存在性与唯一性.同时对相应结论的生态学意义给予了说明.     

一类有投放率系统的控制策略

使用微分方程理论研究了有投放率时一类云杉蚜虫与其天敌模型在相互作用过程中所呈现的动态性质,通过对反馈增益值的选取,得到了系统达到稳定平衡状态的条件,同时保证了实际中蚜虫的密度相对小．     

具有常数收获率的竞争扩散系统的研究

对具有常数收获率的竞争扩散系统进行研究,分别讨论了有扩散和没有扩散时系统所获得的收获,进而得到扩散对收获的影响．     

一类考虑收获的时滞捕食系统的稳定性与Hopf分支研究

给出了一类考虑收获的时滞捕食系统的局部稳定性判断,并由规范型理论和中心流形定理推导出了Hopf分支的方向、稳定性等条件,最后给出了两个数值模拟例子验证了结论的正确性.     

The Visually Mediated Escape Response in Fish: Predicting Prey Responsiveness and the Locomotor Behaviour of Predators and Prey

The outcome of predator-prey encounters is determined by a number of factors related to the locomotor and sensory performance of the animals. Escape responses can be triggered visually, i.e. by the magnifying retinal image of an approaching object (i.e. a predator), called the looming effect, and calculated as the rate of change of the angle subtended by the predator frontal profile as seen by the prey. A threshold of looming angle (ALT, the Apparent Looming Threshold) determines the reaction distance of a startled fish, which is proportional to the attack speed of the predator and its apparent frontal profile. Optimal tactics for predator attacks as well as consideration on their functional morphology are discussed in relation to ALT. Predator optimal attack speeds depend on predator morphology as well as the prey ALT. Predictions on the scaling of ALT suggest that ALT may increase (i.e. implying a decrease in reaction distance) with prey size in cases in which predator attack speeds are high (i.e. > 4 L/s in a 1-m long predator), while it may be relatively independent of prey size when predators attack at lower speeds. The issue of scaling of ALT is discussed using examples from field and laboratory studies. While the timing of the escape is a crucial issue for avoiding being preyed upon, the direction of escape manoeuvres may also determine the success of the escape. A simple theoretical framework for optimal escape trajectories is presented here and compared with existing data on escape trajectories of fish reacting to startling stimuli.     

食饵种群具有收获(存放)率的第Ⅱ类功能性反应模型的定性分析

本文研究了非密度制约的捕食与被捕食系统中被捕食者(食饵)种群具有常数收获(存放)率的第Ⅱ类功能性反应模型的定性性质:当该系统具有存放率时,证明了该系统在一定的条件下极限环的存在性、不存在性及唯一性;当该系统具有收获率时,证明了该系统若存在正平衡点,则它是全局不稳定性.     

Prey nutritional quality and the effectiveness of chemical defenses against tropical reef fishes

Summary Many coral-reef seaweeds and sessile invertebrates produce both secondary chemicals and mineral or fibrous skeletal materials that can reduce their susceptibility to consumers. Although skeletal materials often have been assumed to function as physical defenses, their deterrent effectiveness may derive from their reduction of prey nutritional quality as well as from noxiousness of the skeletal material itself. To test the relative importance of prey nutritional quality and chemical defenses in susceptibility to predation, we offered reef fishes on Guam a choice of artificial foods varying in nutritional quality (4% versus 22% protein) and in secondary chemistry (spanning approximately natural concentration ranges). Field feeding assays were performed with pachydictyol A from the pantropical brown seaweed genus Dictyota, manoalide from the Micronesian sponge Luffariella variabilis, and a brominated diphenyl ether from the Micronesian sponge Dysidea sp. The results indicated that chemical defenses were less effective in high- than in low-quality foods. In paired assays with metabolite-free controls, all three compounds at natural concentrations significantly reduced feeding by reef fishes only in assays using low-quality food, and not in assays with high-quality food. When fishes were offered an array of artificial foods varying in both food quality and metabolite concentration, food quality significantly affected fish feeding in all three cases, while secondary chemistry was significant in only one. Thus differences in nutritional quality, within the natural range among reef organisms, can be comparable to or greater in importance than secondary chemistry in affecting feeding preferences of their consumers. Reduced nutritional quality may be an important selective advantage of producing indigestible structural materials, in addition to their roles as physical support and defense, in coral reef organisms.     

食饵有病的生态-流行病模型的稳定性研究

在考虑捕食者捕食染病的食饵对自身的不利作用的基础上建立了食饵有病的生态-流行病模型,得到了系统平衡点局部渐近稳定的充分条件;讨论了系统的非负不变性、解的有界性,并在此基础上研究了边界平衡点的全局稳定性,得到了平衡点全局稳定的充分条件。