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.     

具有脉冲扩散的近远海渔业系统的周期优化收获策略

研究了一类在周期环境中具有脉冲扩散及收获的近远海渔业系统的动力学行为和优化控制问题.系统中近远海鱼群每隔一定时间进行一次迁移扩散,为了经济利益对近海鱼群进行比例收获.在系统保持周期变化的条件下,选择收获努力量为控制变量,考虑收获成本因素,以一个周期内经济净收益最大为目标研究最优收获策略.首先研究了收获系统周期解的存在性和稳定性,并利用脉冲微分系统的极值原理获得了周期优化控制策略的具体表达式.     

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.     

周期性Gompertz差分模型的最优脉冲收获策略

考虑一个具有周期性脉冲收获的Gompertz差分系统,推导了保证种群系统持续生存、绝灭以及存在全局吸引的正脉冲周期解的充要条件,以一个周期内持续产量最大化为管理目标,通过利用离散的Pontryagin最大值原理获得了最优的脉冲收获策略,推广了现有的结论.     

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.     

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.     

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.      

基于Leslie模型的资源持续利用

传统的Leslie模型是具有年龄结构种群演化的有效研究方法.基于持续收获状态的均匀收获是生物资源可持续利用的重要手段.对均匀收获状态下种群保持稳定的条件进行了研究,证明了均匀收获下稳定状态的充要条件,同时基于该条件,给出了临界稳定状态的判定方法,并就临界稳定状态下种群的分布情况进行了研究.通过引入实际数据并就实际数据进行计算,对该判定条件及最终的种群分布情况进行了实证分析.     

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.     

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.     

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 impulsive harvesting on non-autonomous Beverton–Holt difference equations

Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting.     

Optimal impulsive harvesting on non-autonomous Beverton–Holt difference equations

Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting.     

OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper,the impulsive exploitation of two species periodic competitive system is considered.First,we show that this type of system with impulsive har- vesting has a unique positive periodic solution,which is globally asymptotically stable.Further,by choosing the maximum total revenues as the management objective,we investigate the optimal harvesting policies for periodic competi- tive system with impulsive harvesting.Finally,we obtain the optimal time to harvest and optimal population level.     

Impulsive harvesting and by-catch mortality for the theta logistic model

In this paper, we investigate the population dynamics described by the theta logistic model with periodic impulsive harvesting and by-catch mortality. We examine the existence and stability of two positive periodic solutions by using qualitative methods and cobwebs. Then the sufficient conditions under which the unique positive periodic solution exists and is semi-stable are established, and qualifications for the solutions approach zero are also obtained. Further, choosing the maximum sustainable yield as the management objective, we investigate the optimal harvesting policy for the theta logistic model with periodic impulsive harvesting. Moreover the corresponding theta logistic difference equation is considered subject to the impulsive perturbation, and the dynamics which is parallel to that for the differential equation is examined. The main results extend and generalize the classical results for populations described by the autonomous logistic equation in renewable resources management.     

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.     

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.