一类具周期系数的单种群模型及其最优收获策略

文［１］用直接求解的方法,得到了具周期系数的广义Ｌｏｇｉｓｔｉｃ单种群收获模型的最优收获策略．本文在参照并推广文［２］中一类具周期系数的单种群收获模型周期解的全局渐近稳定性结果的基础上,用变分方法得到了其最优收获策略．所得结果包括了许多常见的自治单种群模型所对应的具周期系数的收获模型,如Ｌｏｇｉｓｔｉｃ型［１］,Ｇｉｌｐｉｎ和Ａｙａｌａ型, Ｇｏｍｐｅｒｔｚ型［３］,以及具类似于Ⅱ,Ⅲ类Ｈｏｌｌｉｎｇ型功能性反应的密度制约函数［４,５］的模型等．     

一类互惠种群脉冲模型的正概周期振荡研究

本文将考虑一类很难得到持续性的概周期互惠种群脉冲模型.利用一种新的研究思想和方法——基于单调算子的不动点理论,我们对其正概周期振荡进行研究并得到一个新的结果;利用李雅普洛夫函数方法,对该模型及其正概周期振荡的全局吸引性进行探讨,得到一些关于该模型正概周期振荡存在、惟一且全局吸引的新结果.本文的结果推广并改进了近年来的一些研究结果.     

非自治时滞Logistic方程的振动性

本文研究了时滞Logistic方程和它的线性化方程的振动性。在一定的条件下,我们证明了这两个方程在振动性上等价．所得结果推广和改进了〔1〕的相应结果,同时也给〔2〕的作者提出的问题一个肯定的回答．     

具有可变时滞的非自治离散Logistic方程的全局吸引性

得到了具有可变时滞的非自治离散Logistic方程的正解收敛于方程的正平衡常数的一系列充分条件和振动准则．     

固定周期脉冲微分方程到状态依赖脉冲的转化及应用

本文研究了一类二维状态依赖脉冲微分方程的阶1周期解存在性和轨道稳定性条件．然后,将一维固定周期脉冲的微分方程转化为二维状态依赖脉冲微分方程,研究其阶一周期解的存在性和稳定性．作为应用,我们研究了固定周期常数收获的Logistic方程的动力学性质,以及两个固定周期注射药物单室扩散模型的动力学性质．     

单种群非自治缀块扩散的竞争模型的概周期解

本文考虑单种群非自治缀块扩散的竞争系统,利用微分不等式,证明了系统存在唯一的正概周期解,它在壳的扰动下是稳定的．     

关于Malthus方程和logistic方程的统一表达式

崔启武在文［1]简称《结构》中,再一次认为他所获得的描述种群增长的模型包含了Malthus方程和Logistic方程．这一错误的结论,最早出现在1982年崔启武和G．Lawson合写的论文[2]简称《扩充》中,后来又在文[3]（简称《答疑》）中得到进一步的发挥．本文从《结构》、《扩充》,《答疑》中出现的主要错误说起,论证崔启武的模型并非Malthus和Logistic方程的统一表达式．     

非自治Lotka—Volterra型竞争系统的一些新结果

研究一般非自治 Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ型 ｎ个种群相互竞争生态系统的定性性质．建立了关于一部分种群灭绝，而另一部分种群一致持续生存与全局渐近稳定的一系列新的判别准则．这些结果改进和推广了文献［２，３］中的主要结果。     

广义Schumacher模型的改进及其应用

通过对前人提出的生长方程的具体分析,提出了一种改进的Schumacher生长方程．该模型包含了Gompenz函数、Schumacher方程及广义Schumacher方程,具有很强的自适应性和实用性．采用遗传算法。利用该模型对珍稀植物长苞铁杉和侧柏生长资料分别进行了拟合．结果表明,改进的Schumacher方程的拟合精度明显优于Schumache,方程和广义Schumacher方程,也优于经典的Logistic模型和李新运等自适应模型。可以在林木生长动态模拟及种群增长动态研究中广泛应用．     

具有反馈控制的非自治多种群捕食-被捕食系统的持久性与全局吸引性

研究具有反馈控制的非自治多种群捕食-被捕食系统的持久性与全局吸引性.通过引入函数上、下平均的概念,得到系统持久和全局吸引的均值条件,同时将文献[7]的结果推广到了时滞非自治系统上.     

Bio-economics of a renewable resource in a seasonally varying environment

In this paper we study the bio-economics of a renewable resource with governing dynamics described by two distinct growth functions (viz., logistic and Gompertz growth functions) in a seasonally varying environment. Seasonality is introduced into the system by taking the involved ecological parameters to be periodic. In this work, we establish a procedure to obtain the optimal path and compute the optimal effort policy which maximizes the net revenue to the harvester for a fairly general optimal control problem and apply this procedure to the considered models to derive some important conclusions. These problems are solved on the infinite horizon. We find that, for both the models, the optimal harvest policy and the corresponding optimal path are periodic after a finite time. We also obtain optimal solution, a suboptimal harvesting policy and the corresponding suboptimal approach path to reach this optimal solution. The key results are illustrated using numerical simulations and we compare the revenues to the harvester along the optimal and suboptimal paths. The general procedure developed in this work, for obtaining the optimal effort policy and the optimal path, has wider applicability.     

Harvesting in a resource dependent age structured Leslie type population model

We analyse the effect of harvesting in a resource dependent age structured population model, deriving the conditions for the existence of a stable steady state as a function of fertility coefficients, harvesting mortality and carrying capacity of the resources. Under the effect of proportional harvest, we give a sufficient condition for a population to extinguish, and we show that the magnitude of proportional harvest depends on the resources available to the population. We show that the harvesting yield can be periodic, quasi-periodic or chaotic, depending on the dynamics of the harvested population. For populations with large fertility numbers, small harvesting mortality leads to abrupt extinction, but larger harvesting mortality leads to controlled population numbers by avoiding over consumption of resources. Harvesting can be a strategy in order to stabilise periodic or quasi-periodic oscillations in the number of individuals of a population.     

Random effects in population models with hereditary effects

This paper discusses the influence of environmental noise on the dynamics of single species population models with hereditary effects. A detailed analysis is carried out for the logistic equation with discrete delay in the resource limitation term (Hutchinson's equation). When the system undergoes Hopf bifurcation, we find the stationary probability density distribution for the amplitude of the periodic solution by means of an averaged Fokker-Planck equation. Finally, we estimate the persistence time of the species when the population density has a lower bound beyond which it goes extinct.     

Lotka-Volterra方程的概周期解的存在性

本文讨论具有概周期系数的Lotka-Volterra微分方程.给出该微分方程存在大于零的概周期解的一个实用、简沽的充分条件.     

Metapopulation dynamics for spatially extended predator–prey interactions

Traditional metapopulation theory classifies a metapopulation as a spatially homogeneous population that persists on neighboring habitat patches. The fate of each population on a habitat patch is a function of a balance between births and deaths via establishment of new populations through migration to neighboring patches. In this study, we expand upon traditional metapopulation models by incorporating spatial heterogeneity into a previously studied two-patch nonlinear ordinary differential equation metapopulation model, in which the growth of a general prey species is logistic and growth of a general predator species displays a Holling type II functional response. The model described in this work assumes that migration by generalist predator and prey populations between habitat patches occurs via a migratory corridor. Thus, persistence of species is a function of local population dynamics and migration between spatially heterogeneous habitat patches. Numerical results generated by our model demonstrate that population densities exhibit periodic plane-wave phenomena, which appear to be functions of differences in migration rates between generalist predator and prey populations. We compare results generated from our model to results generated by similar, but less ecologically realistic work, and to observed population dynamics in natural metapopulations.     

The Beverton–Holt q-difference equation

The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures.     

Establishment of new mutations in changing environments

Understanding adaptation in changing environments is an important topic in evolutionary genetics, especially in the light of climatic and environmental change. In this work, we study one of the most fundamental aspects of the genetics of adaptation in changing environments: the establishment of new beneficial mutations. We use the framework of time-dependent branching processes to derive simple approximations for the establishment probability of new mutations assuming that temporal changes in the offspring distribution are small. This approach allows us to generalize Haldane's classic result for the fixation probability in a constant environment to arbitrary patterns of temporal change in selection coefficients. Under weak selection, the only aspect of temporal variation that enters the probability of establishment is a weighted average of selection coefficients. These weights quantify how much earlier generations contribute to determining the establishment probability compared to later generations. We apply our results to several biologically interesting cases such as selection coefficients that change in consistent, periodic, and random ways and to changing population sizes. Comparison with exact results shows that the approximation is very accurate.     

Optimal harvesting of prey–predator system with interval biological parameters: A bioeconomic model

The paper presents the study of one prey one predator harvesting model with imprecise biological parameters. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. We identify the equilibrium points of the model and discuss their stabilities. The existence of bionomic equilibrium of the model is discussed. We study the optimal harvest policy and obtain the solution in the interior equilibrium using Pontryagin’s maximum principle. Numerical examples are presented to support the proposed model.     

Age-structured optimal control in population economics

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (both age-dependent). By using a new maximum principle for age-structured control systems we derive meaningful results for the optimal migration and saving rate in an aging population. The model used in the numerical calculations is calibrated for Austria.