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1.
研究了一类具有食饵避难的Leslie-Gower捕食与被捕食系统收获模型,利用Hurwitz判据,得到了正平衡点局部渐近稳定,进一步构造了适当的Lyapunov函数,证明了正平衡点的全局渐近稳定性.并且在捕获努力量假说下,对发生食饵避难的两种群同时捕获,考虑了生态经济平衡点的存在性和利用Pontryagin最大值原理对两种群进行最优收获,得到当贴现率为零时,既保持了生态平衡,又使得在渔业开发过程中取得最大经济利益.  相似文献   

2.
利用微分方程的定性理论和Pontryagin最大值原理,讨论了一类食饵-捕食者种群都具有密度制约并且都具有收获的HollingⅡ型功能反应模型的性质,得到了存在边界平衡点、唯一正平衡点及各平衡点全局渐进稳定的条件,分析了相应的生物学意义,给出了最优可持续收获策略,并且用mathematica对特定参数下的系统进行了模拟.  相似文献   

3.
讨论一类具有收获且食饵染病的传染病模型,考虑了Holling Ⅱ类功能性反应及饱和发生率.利用Routh-Hurwitz判据研究了非负平衡点的局部稳定性,通过构造Lyapunov函数得到平衡点全局渐近稳定的充分条件.最后,利用Pont ryagin最大值原理研究最优收获策略.  相似文献   

4.
研究了具有非线性收获及食饵避难的Leslie-Gower模型,讨论了该模型解的正性、有界性及正平衡点的存在性.通过分析特征方程并运用Routh-Hurwitz判别法,得出正平衡点局部渐近稳定的充分性条件.借助Lyapunov函数以及LaSalle不变原理,研究了正平衡点的全局稳定性.利用Pontryagin最大值原理,得到了最优税收τoptimal以及最优平衡解(xoptimal,yoptimal,Eoptimal).数值模拟与理论结果一致.  相似文献   

5.
对一类两种群均有线性收获率的具HollingII类功能反应的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,得到此类生物捕食系统的平衡点的性态和极限环的存在,不存在的条件,从而对更具一般性的一类具有非常数收获率的食饵-捕食系统作了较为全面的定性分析,补充完善了前人的结果.  相似文献   

6.
对一类两种群均有收获率的具较为特殊的功能反应函数的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,此类生物捕食系统平衡点的性态和极限环的存在,不存在及唯一的条件,获得了一类食饵-捕食系统的定性分析结果.  相似文献   

7.
食饵种群具有常数收获率的捕食—食饵模型分析   总被引:3,自引:0,他引:3  
陆忠华  陈兰荪 《数学杂志》1994,14(4):549-558
本文研究食饵种群具有常数收获效的捕食-食饵模型:{dx/dt=bx^2(1-x/k)-βxy-hdy/dt=-cy+dxy讨论了极限环的存在性、唯一性和正平衡点的全局稳定性以及分界线环的存在性。  相似文献   

8.
建立并分析了疾病在食饵中传播、食饵考虑避难所效应的捕食与被捕食模型,捕食者不仅捕食感染食饵而且捕食易感食饵.讨论了系统的有界性和各平衡点的存在性,利用Routh-Hurwitz判据分析各平衡点的局部渐进稳定性,通过构造Lyapunov函数证明了各平衡点的全局渐进稳定性,并进行数值模拟以验证结论的正确性.  相似文献   

9.
李蒙  陈伯山  李必文 《数学杂志》2016,36(5):993-1004
本文研究了一类同时带有非线性食饵收获和捕食者妊娠时滞的微分代数捕食者-食饵系统的稳定性及Hopf分支问题.利用了分支理论和稳定性理论,以捕食者妊娠时滞作为系统的分支参数,获得了所提出的新系统在正平衡点处系统稳定性的相关判据条件和Hopf分支的产生条件.推广了一般带有线性收获和时滞的微分代数捕食者-食饵系统的结论.  相似文献   

10.
具有年龄结构的捕食种群系统的最优收获策略   总被引:1,自引:0,他引:1  
分析了一类基于年龄结构的食饵-捕食者系统的最优收获问题.证明了系统非负解的存在唯一性、解对控制变量的连续依赖性.讨论了最优策略的存在性,利用法锥和Dubovitskii-Milyutin理论导出了最优性条件.  相似文献   

11.
Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.  相似文献   

12.
基于年龄结构的种群系统的最优收获控制   总被引:1,自引:0,他引:1  
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.  相似文献   

13.
Introduction' There have recently appeared in the literature several mathematical models of stagestructured population growth, i. e., models which take into account the faCt that individuals in a population may belong to one of two classes, the immatures and the matureslllZI.Cannibalism has been observed in a great variety of species, including a number of fish species.Cannibalism models of various types have also been investigatedI3"l. In these models, the ageto maturity is represented by a…  相似文献   

14.
The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.  相似文献   

15.
This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique.  相似文献   

16.
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.  相似文献   

17.
In this article bio-economics of a renewable resource that is subjected to strong Allee effect (multiplicative Allee effect) is investigated from sole owner perspective. The considered optimal harvesting problem has been solved using Pontryagin maximum principle. The control problem admits multiple singular equilibrium solutions in contrast to the case where the growth of the resource is of compensatory nature. Thus the choice of optimal singular solution and the nature of associated approach paths make the problem pertinent and interesting.  相似文献   

18.
In this model we discuss the bioeconomic harvesting of a prey–predator fishery in which both the species are infected by some toxicants released by some other species. Here both the species are harvested where we use the usual catch-per-unit-effort hypothesis. The dynamical behaviour of the exploited system is examined. The possibility of existence of a bionomic equilibrium is considered. The optimal harvesting policy is studied by using Pontryagin’s maximal principle. Some numerical examples and the corresponding solution curves are studied to illustrate the results of the model. Finally, the existence of limit cycle is discussed.  相似文献   

19.
An optimal policy is sought for maximizing present value from the combined harvest of two ecologically dependent species, which would coexist as predator and prey in the absence of harvesting. Harvest rate for each species is assumed proportional to both stock level and effort. For a large class of biological productivity functions, it is established that the optimal equilibrium point in the phase-plane of stock levels must be a saddle-point. For quadratic productivity functions, a combination of analytical reasoning and numerical experiment is used to show that first and second order necessary conditions for optimality are satisfied by a unique approach to equilibrium, which must therefore be optimal. The corresponding control law is given, and an apparent suggestion of two previous authors concerning the policy is shown to be inappropriate. The optimal policy enables an estimate to be made of the true loss of resource value due to a catastrophic fall in stock level.  相似文献   

20.
A multispecies harvesting model with mutual interactions is formulated based on Lotka–Voltera model with three competing species which are affected not only by harvesting but also by the presence of prey, predator and the third species, which is super predator. In order to understand the dynamics of the system, it is assumed that the super predator follows the logistic growth. Further, there is demand for all the above three species in the market and hence harvesting of all species is performed. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin’s maximal principle. Finally some numerical examples are discussed to illustrate the model.  相似文献   

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