一类生物种群经济捕获模型

本文继续文[1]的工作,进一步讨论了系统     

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.     

开发生物资源的最优策略

以dx/dt=rx(1-x/k)-E(t)x为模型,讨论在[0,T]时间内,在初始条件x0和终端条件xT限制下,对生物资源进行开发的最优策略。     

具空间扩散的时变种群系统的最优捕获控制

讨论了一类时变种群扩散系统的最优捕获控制的非线性问题,证明了最优捕获控制的存在性,并给出了控制u（t,x）∈Uad为最优的必要条件和最优性组．     

具有函数放养率或捕获率天敌有种内竞争系统的稳定性

本文讨论具有函数放养率或捕获率且天敌有种内竞争系统的稳定性．具体研究雌寄生蜂与寄主生态系统．进行了稳定性分析,种群灭绝分析,指出了理论上和实践意义．     

环境污染下基于最优捕获策略的近海-远海捕鱼模型的动力学性质(英文)

近年来,由于人类的过度开发,使得海洋资源(尤其是近海海洋资源)急剧下降,加上日益严重的海洋污染,给海洋资源管理带来很大的困难.为了更好的管理和利用海洋资源,本文考虑到环境污染中脉冲扩散对种群的影响,建立了一个近海-远海渔业模型,给出了正周期解存在性及平凡周期解和正周期解全局渐近稳定性的充分条件.进一步,在环境污染的情况下,给出了最优捕获策略,得到了最大持续产量和相应的捕获努力量.最后,通过数值模拟证实了我们所得的结论的正确性.     

具有时滞和阶段结构的捕食-被捕食模型及最优捕获策略

研究了一个具有阶段结构和时滞的捕食-被捕食模型.分析了它的局部性质。得到某些非负平衡点全局稳定的充分条件,其中用到李雅普诺夫函数及其他方法．最后,在内部平衡点全局稳定的情况下,得出了最优捕获策略．     

稳定有界的Logistic方程的最优捕获策略

考虑单种群非自治的Logistic方程的开采问题．在R^ 中都存在均值的意义下,作为周期和概周期函数的推广,首先给出稳定有界函数的概念．然后定义一个新的最终最优收获策略用于处理我们的问题．选择单位时间的最大持久收益的极限均值作为管理目标。同时得到了最佳的种群水平．作为应用,我们以概周期系数的Logistic方程为例,表明我们的结果不仅推广了经典的Clark关于自治的Logistic方程的收获问题,而且推广了范猛和王克的关于周期的Logistic方程的收获问题的结果．     

一类生态系统的脉冲控制

利用脉冲系统的线性近似判定的方法对一个具有脉冲控制的生物模型进行研究,得到了使其渐近稳定到原先不稳定的平衡点的充要条件并给出了生态解释。     

一个增加渔业产量的最优策略

本文研究了Logistic模型在渔业收获中的应用．我们脉冲的在湖泊中增加鱼的食物（水草）,以此来增大湖泊的环境容纳量．因此,经过一段时间后,鱼的数量可以达到一个很高的水平．我们从生态和经济学的角度出发,找到了最优策略,通过例子（表1一表10）给出了具体的策略．在最后一个例子（表11）中,我们比较了参数A和T对模型的不同影响．最后,我们指出了本文的数学和数值模拟结果在生态学和经济学中的应用,并且作了简短的讨论．     

A Bifurcation Analysis of a Differential Equations Model for Mutualism

We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model [Dean, A.M., Am. Nat. 121(3), 409–417 (1983)], but corrects problems due to singularities in that model. In addition, we investigate our model in more depth by varying the intrinsic growth rate for each of the species and analyzing the resulting bifurcations in system behavior. We are especially interested in transitions between facultative and obligate mutualism. The model reduces to the familiar Lotka–Volterra model locally, but is more realistic for large populations in the case where mutualist interaction is strong. In particular, our model supports population thresholds necessary for survival in certain cases, but does this without allowing unbounded population growth. Experimental implications are discussed for a lichen population.     

一类离散Lotka-Volterra系统的灭绝和稳定性（英文）

考虑了一类受有毒物质影响的两物种非自治离散Lotka-Volterra系统.在平均增长率意义下,得到了其中一种物种灭绝的充分条件,证明了另外一种物种的稳定性.     

离散广义Logistic模型的混沌控制

利用Lyapunov指数方法,验证了一类离散广义Logistic模型存在混沌现象,并采用混沌控制中OGY方法的基本思想,研究了这类模型的混沌控制问题,得出了消除混沌,保持种群稳定到不动点和2-周期轨道的充分条件．     

Optimal Strategies for Managing Wildlife Harvest Under System Change

Wildlife populations are experiencing shifting dynamics due to climate and landscape change. Management policies that fail to account for non-stationary dynamics may fail to achieve management objectives. We establish a framework for understanding optimal strategies for managing a theoretical harvested population under non-stationarity. Building from harvest theory, we develop scenarios representing changes in population growth rate () or carrying capacity () and derive time-dependent optimal harvest policies using stochastic dynamic programming. We then evaluate the cost of falsely assuming stationarity by comparing the outcomes of forward projections in which either the optimal policy or a stationary policy is applied. When declines over time, the stationary policy leads to an underharvest of the population, resulting in less harvest over the short term but leaving the population in a higher-value state. When declines over time, the stationary policy leads to overharvest, resulting in greater harvest returns in the short term but leaving the population in a lower and potentially more vulnerable state. This work demonstrates the basic properties of time-dependent harvest management and provides a framework for evaluating the many outstanding questions about optimal management strategies under climate change. Published 2021. This article is a U.S. Government work and is in the public domain in the USA.     

The controlled assembly of microcosmic communities: the selective extinction hypothesis

Summary Forty communities were assembled through the controlled inoculation of algae, protozoans and a rotifer according to either of 2 distinct introduction schedules. These introduction schedules were constructed such that species reinvaded on average either every 6 or 8 w. Ten of the 20 beakers experiencing each invasion schedule contained 300 ml of media; the remaining beakers in each invasion category contained 100 ml of media. Species richness consistently increased throughout the initial 4 w and 7 w of the experiment for the low and high invasion rate beakers, respectively. The numbers of species in the low rate beakers were uncorrelated with time during the last half of the experiment; however, species richness gradually declined during this period in the high rate beakers. The extinction rate is shown to be disproportionately higher for large organisms in the small microcosms. Such selective extinction is consistent with the MacArthur-Wilson equilibrium model.     

一类功能性反应模型在常数收获下的动态特性

具有功能性反应的捕食与被捕食模型具有非常复杂的动态性质．特别是在常数收获下,该模型呈现了各种各样、纷杂多变的动态特性。其中包括正平衡点及其稳定性的变化、各种分叉的产生以及周期解和极限环的出现．本文重点研究了常数收获项对一类功能性反应模型的动态性能的影响,得到了该收获模型存在稳定正平衡点、产生分叉以及在Hopf分叉附近产生周期解和极限环的若干充分条件．     

年龄相关的种群系统的最优生育率控制

讨论了一类与年龄相关的时变种群系统最优生育率控制的非线性问题,利用Ba- nach空间的Saks-Masur引理,证明了系统最优生育率控制的存在唯一性,并得到了控制为最优的必要条件和最优性组．所得结果可为种群系统控制问题的实际研究提供必要的数学理论基础．     

Population and Harvest Dynamics of Midcontinent Sandhill Cranes

Sandhill cranes (Antigone canadensis) inhabiting the midcontinent of North America have been hunted since the 1960s under management goals of maintaining abundance, retaining geographic distribution, and maximizing sustainable harvest. Some biologists have raised concerns regarding harvest sustainability because sandhill cranes have lower reproductive rates than other game birds. We summarized demographic information in an age-structured matrix model to better understand population dynamics and harvest. Population indices and recovered harvest since the early 1980s suggest midcontinent sandhill cranes have experienced an average long-term annual growth of 0.9%; meanwhile, harvest has increased 1.8% annually. Adult survival and recruitment rates estimated from field data required modest adjustments (1–3%) so that model-derived growth rates matched growth estimated from a long-term survey (0.887 adult survival and 0.199 females/breeding female). Considering 0.9% long-term annual growth, sandhill cranes could be harvested at a rate of 6.6% if harvest was additive to natural mortality (assumed to be 0.05) or 11.3% if harvest mortality compensated for natural mortality. Life-history characteristics for long-lived organisms and demographic evidence suggested that hunter harvest was primarily additive. Differential harvest rates of segments of sandhill cranes in the midcontinent population derived from differential exposure to hunting suggested potentially unsustainable harvest for greater sandhill cranes (A. c. tabida) from 2 breeding segments. Overall, demographic evidence suggests that the harvest of sandhill cranes in the midcontinent population has been managed sustainably. Monitoring activities that reduce nuisance variation and estimate vital and harvest rates by subspecies would support continued management of sandhill cranes that are of interest to hunters and bird watchers. Published 2020. This article is a U.S. Government work and is in the public domain in the USA.