自治单种群模型及其最优捕获策略

本文用一种新的方法,讨论了单种群生物资源的捕获优化问题.分别以单位时间最大可持续捕获量和单位时间最大净利润为管理目标,得到一类自治单种群捕获模型的最优捕获策略,所得结果包括了文献中研究过的几乎所有自治单种群捕获模型的相应研究结果.     

一类自治单种群模型及其最优捕获策略

用一种新的方法,讨论了单种群生物资源的捕获优化问题.分别以单位时间最大可持续捕获量和单位时间最大净利润为管理目标,得到一类自治单种群捕获模型的最优捕获策略,所得结果包括了文献中研究过的几乎所有自治单种群捕获模型的相应研究结果.     

广义Richards-Gilpin-Ayala模型的捕获优化问题

在Richards-Gilpin-Ayala模型的基础上,提出了一类更广泛的数学模型—广义Richards-Gilpin-Ayala模型.进而讨论该模型单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质.在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式.这些结果推广了相关文献中关于Schaefer模型、广义Logistic模型的相应结果.     

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.     

阶段结构单种群捕获的优化策略

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.同时,对经济学中的Gordon理论进行分析.     

一类随机模型的最优捕获问题研究

在Volterra两种群竞争模型的基础上,构造了随机的具有捕获的两种群竞争模型,研究讨论了捕获对种群生长过程的影响和如何实现最优捕获等问题.从确定性模型入手,深入讨论随机竞争模型的收获最优问题.通过对捕获强度E和贴现率等的估计与讨论,计算出了最优捕获强度最优捕获量最优经济收益.     

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.     

互惠系统的最优脉冲捕获

对两种群互惠系统的脉冲捕获问题进行了全面的研究.确定了在被捕获种群达到一定数量时,再进行脉冲捕获的最优捕获策略.这样既维持了种群的生态平衡,又使我们在捕获过程中的获利最大.     

动态价格下Logistic生长模型的捕获问题

基于市场价格受供给和需求影响,建立一种新型的动态价格下的捕获模型,并对此模型进行了动力学分析.在经济意义下,如果捕获相同数量的生物种群,那么在均衡价格下的捕获努力量会低于常数价格下的捕获努力量,这将为如何降低捕捞成本提供有价值的理论借鉴.     

一类半线性时变种群系统的最优捕获控制

讨论了年龄相关的半线性时变种群系统的最优捕获控制问题.根据微积分方程及泛函分析的知识证明了最优捕获控制的存在性,得到了捕获控制为最优的必要条件.     

Asymptotically periodic solution and optimal harvesting policy for Gompertz system

In this paper, the single species modelled by (asymptotically) periodic Gompertz equation is investigated. It is shown that the (asymptotically) periodic system has a unique (asymptotically) periodic solution which is globally asymptotically stable for the positive solution. When the nonautonomous Gompertz equation is subject to harvesting, we study the optimal harvesting policy for the periodic system and obtain the corresponding optimal population level and the maximum sustainable yield. Further, when the functions in the exploited Gompertz system are stably bounded functions, we study the ultimately optimal harvesting policy. By choosing the average limiting maximum sustainable yield as management objective, the corresponding optimal population level is determined.     

Optimal harvesting policy for stochastic Logistic population model

In this paper, we consider some optimal harvesting policies for single population models, in which the harvest effort and the intrinsic growth rate are disturbed by environment noises. We choose the maximum sustainable yield and the maximum retained profits as two management objectives, and obtain the optimal harvesting policies, respectively. For the two objectives, we give the optimal harvest effort that maximizes the sustainable yield (or retained profits), the maximum of expectation of sustainable yield (or retained profits) and the corresponding variance. Their explicit expressions are determined by the coefficients of equation and the disturbance intensity.     

Optimal impulsive harvesting policy for single population

In this paper, we established the exploitation of impulsive harvesting single autonomous population model by Logistic equation. By some special methods, we analysis the impulsive harvesting population equation and obtain existence, the explicit expression and global attractiveness of impulsive periodic solutions for constant yield harvest and proportional harvest. Then, we choose the maximum sustainable yield as management objective, and investigate the optimal impulsive harvesting policies respectively. The optimal harvest effort that maximizes the sustainable yield per unit time, the corresponding optimal population levels are determined. At last, we point out that the continuous harvesting policy is superior to the impulsive harvesting policy, however, the latter is more beneficial in realistic operation.     

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.     

周期Gompertz生态系统中的最优脉冲控制收获策略

以周期Gompertz系统为基础,讨论了周期变化的单种群生物资源的收获优化问题及种群的动力学性质.在单位收获努力量假设下,以最大可持续收获量为管理目标,确定了线性收获下的最优收获策略,获得了最优收获努力量、最大可持续收获及相应的最优种群水平的显示表达式,为自然资源的开发和利用提供了理论依据.     

PERSISTENCE IN DISCRETE MODELS OF A POPULATION WHICH MAY BE SUBJECTED TO HARVESTING

We consider a class of one-dimensional maps as discrete models of a single population. A general criterion for persistence of a population is obtained, and this criterion is shown to be valid for many models proposed in the literature. These results are extended to models which are periodic and to models which include constant rate harvesting.     

Optimal harvesting policies for periodic Gompertz systems

In this paper, we study the periodic Gompertz system with harvesting. First, we analyze the system with continuous harvesting and obtain the maximum annual-sustainable yield, the optimal harvesting effort and the optimal population level for such a system. Then, the harvesting is assumed to occur at fixed moments every year, and we establish the Gompertz system with impulsive perturbation. And we investigate the impulsive harvesting policy to maximize the annual yield and to keep the population sustainable development. At last, the optimal results of the impulsive harvesting system are compared with those of the continuous harvesting system.