基于弹性增长的尺度结构种群的最优平衡收获

本文研究一类个体尺度具有弹性增长行为的种群模型的平衡态收获问题,种群加权总规模对个体生死率的影响各异.运用Ascoli-Arzela定理确立了最优解的存在性,借助针状变分法导出极值原理.最后通过对转换函数平衡态水平的细致分析,证明了最优策略的唯一性.     

模拟周期环境和尺度结构的种群系统的最优收获率

研究一类周期环境中基于个体尺度分布的种群资源模型的最优收获率问题.运用泛函分析方法证明了最优策略的存在性,借助非线性分析中的切锥-法锥技巧导出了最优策略的结构,为模型应用奠定了理论基础.     

基于尺度结构的捕食-食饵种群系统的最优收获率北大核心CSCD

文章研究了基于尺度结构的捕食-食饵种群系统的最优收获率控制问题,通过控制种群的收获率使得种群分布达到理想状态并使收获成本最小.首先借助不动点定理证明了系统解的存在唯一性,其次导出共轭系统并利用切锥-法锥理论给出了收获控制为最优的必要性条件.     

依赖个体尺度结构的种群资源开发模型理论分析

研究一类具有个体尺度结构的非线性种群控制模型.确立了状态系统模型非负解的存在唯一性,以及状态关于控制变量的连续依赖性.应用紧性推理和极值化序列法证明了最优策略的存在性,借助切锥法锥和共轭系统技巧导出了最优性条件.     

周期环境中捕食者具有尺度结构的三物种捕食-食饵系统的最优收获

对种群动力学及相关控制问题的研究,不仅具有理论意义,而且与生物多样性保护、病虫害防治及可再生资源的开发利用密切相关.该文研究了一类周期环境中具有两相互竞争食饵和一捕食者的三物种捕食 食饵系统的最优收获,其中捕食者具有尺度结构且用一阶偏微分方程描述.运用不动点定理证明了系统非负有界解的存在唯一性,并讨论了解关于控制变量的连续依赖性.应用切 法锥技巧导出最优收获条件,并借助Ekeland变分原理讨论了最优策略的存在唯一性.这里目标泛函表示收获三物种产生的净经济效益.所得结果将有利于可再生资源的开发.     

一类具有阶段结构的捕食-食饵种群收获模型

本文研究了一类具有阶段结构和密度制约的捕食-食饵两种群同时收获模型.利用比较定理,Barbalt引理,极人值原理等,获得了平衡点稳定性的充分条件,以及在不同情况下,各种群以最大可持续收获量为管理目标的最优生存量和最大收获量.     

一类种群系统的适定性及最优收获问题

本文研究了一类非线性时变种群扩散系统的适定性及最优收获问题.利用压缩不 动点原理讨论了该种群系统的解的存在唯一性.证明了最优收获控制的存在性,并且获 得了最优控制的唯一性和所满足的必要条件.     

具有尺度结构的种群混合系统的最优投放控制

研究一类具有尺度结构的害鼠种群最优不育控制问题,状态系统模型由一个带全局反馈边界条件的一阶偏微分方程和两个常微分方程组成,控制函数为时变不育剂投放量,性能指标代表害鼠终端规模、环境中不育剂残留量以及控制成本的加权和.首先确立状态系统非负有界解的存在唯一性,并给出状态向量函数关于控制变量的连续依赖性;其次构造共轭系统和关联法锥,导出精确刻画最优策略的Euler-L agrange方程;最后运用Ekeland变分原理和不动点方法证明最优策略的存在唯一性.文章为害鼠不育控制提供一种新的建模方法.     

与年龄相关的非线性种群系统的最优收获控制

讨论与年龄相关的一类非线性种群系统的最优收获控,运用泛函分析的Mazru's定理证明了最优收获控制的存在性,利用G-微分和Lions的变分不等式理论,导出了控制为最优的必要条件,得到了由积分-偏微分方程和变分不等式组成的最优性组,由最优性组确定最优控制.     

具有年龄结构的线性周期种群动力系统的最优收获控制问题

研究一类具有年龄结构的线性周期种群动力系统的最优收获控制问题,即讨论了具有周期的生死率和周期变化的收获项的Lotka Mckendrick模型.利用Mazur's定理,作者证明了控制问题最优解的存在性,同时借助于法锥概念,还得到了控制问题最优解存在的必要条件。最后，在适当的假设下，得到了最优控制问题的唯一解。该文的结论推广了某些已有的结果.      

Quadratic harvesting dominated optimal strategy for a stochastic single-species model

A stochastic population model with the mixed harvesting strategy is formulated and studied in this paper. Sufficient and necessary conditions for survival of the species are derived firstly. Then, based on the ergodic stationary distribution, the optimal strategy is identified. Results show that the linear harvesting effort threatens to the survival of the species; the quadratic harvesting strategy occupies an absolute advantage in the harvesting and excludes the linear part out of the optimal harvesting strategy. It''s interest to see all these occur only in the random environments. Computer simulations are carried out to support the obtained results.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

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.     

Optimal harvesting of a Gompertz population model with a marine protected area and interval‐value biological parameters

To protect fishery populations on the verge of extinction and sustain the biodiversity of the marine ecosystem, marine protected areas (MPA) are established to provide a refuge for fishery resource. However, the influence of current harvesting policies on the MPA is still unclear, and precise information of the biological parameters has yet to be conducted. In this paper, we consider a bioeconomic Gompertz population model with interval‐value biological parameters in a 2‐patch environment: a free fishing zone (open‐access) and a protected zone (MPA) where fishing is strictly prohibited. First, the existence of the equilibrium is proved, and by virtue of Bendixson‐dulac Theorem, the global stability of the nontrivial steady state is obtained. Then, the optimal harvesting policy is established by using Pontryagin's maximum principle. Finally, the results are illustrated with the help of some numerical examples. Our results show that the current harvesting policy is advantageous to the protection efficiency of an MPA on local fish populations.     

Existence and exponential convergence of almost periodic positive solution for Nicholson's blowflies discrete model with linear harvesting term

This paper deals with a discrete Nicholson's blowflies model with linear harvesting term. By using contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of unique almost periodic positive solution. Moreover, we investigate exponential convergence of the almost periodic positive solution by Lyapunov functional. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal harvesting for a stochastic logistic model with S-type distributed time delay

In this paper, the optimization problem of harvesting for a stochastic logistic model with S-type distributed time delay (which contains both discrete time delay and continuously distributed time delay) is studied by using ergodic method.     

Pseudo almost periodic dynamics of delay Nicholson's blowflies model with a linear harvesting term

In this paper, we investigate a class of delay Nicholson's blowflies model with a linear harvesting term, new criteria for the existence and convergence dynamics of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic function, together with constructing suitable Lyapunov functionals. The obtained results extend previously known results, and they also partially answer an open problem proposed by L. Berezansky et al. Finally, an example with simulation is presented to demonstrate the effectiveness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting

This paper is concerned with a delayed Nicholson's blowflies model with discontinuous harvesting, which is described by an almost periodic nonsmooth dynamical system. Under some reasonable assumptions on the discontinuous harvesting function, by using the Filippov regulation techniques and the theory of dichotomy, together with the Halanay inequality, we establish some new criteria on the existence of positive almost periodic solution and its convergence. An example with numerical simulation is also presented to support the theoretical results.     

Dynamic model and simulation analysis of the genetic impact of population harvesting

In this paper the impact of exploitation of a sexually reproducing population is investigated by means of a selection model. Our aim is to find genetic systems for which the fishing results in selection effect, provided that the growth and reproduction rates of individuals are genetically determined. To this end a complex dynamic model is presented, providing long-term predictions both on the size structure and on the genetic composition of the population. For a minimal nontrivial model, the two-locus two-allele case is considered, where the survival, transition and reproduction rates depend on size and genotype. For each size class and genotype the corresponding density is a state variable. The mating system is supposed to be totally panmictic and the gamete production is described in terms of the meiosis matrix.Based on the above model, an in silico analysis is carried out. The simulation results show that the long-term behaviour of the genetic structure can be characterized by a cyclic convergence, which means that the state sequences corresponding to different phases of the reproduction cycle tend to an asymptotic genotype distribution. For an illustration of the effect of exploitation on the genetic composition the “fishing effort” model is considered. If the totally homozygous genotype possesses the best phenotype, fishing does not seem to influence the genetic distribution in the long term. The same is true in case of heterozygote advantage. In some situations, however, fishing modifies the genetic distribution of the population. Meanwhile there is a significant change in the size of the harvested individuals. This result points out to the importance of the genotype-phenotype correspondence while building up fishing strategies.     

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.