Optimal Harvesting and Stability for a Predator-prey System with Stage Structure

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.     

A PREDATOR-PREY SYSTEM WITH STAGE STRUCTURE AND HARVESTING FOR PREDATOR

In this paper, we consider a predator-prey system with stage structure and harvesting (where the predator population has two stages, an immature stage and a mature stage with harvesting, and the growth of the prey population is of Lotka-Volterra nature). We obtain the conditions of the globally asymptotic stability for three nonne-gative equilibria of this system.     

具有阶段结构的竞争系统的持久性和稳定性

研究带有时滞和成长阶段的两种群竞争模型,第一个种群分成年和幼年两个阶段,第二个种群不具有阶段结构.本文证明了系统正解的有界性;利用比较原理得到了系统永久生存的充分条件;通过构造Lyapunov函数得到了系统全局渐近稳定的充分条件.     

一类具有阶段结构的三种群竞争系统

对一类具有阶段结构的三种群竞争系统进行了分析,得到了边界平衡点的全局渐近稳定性条件.     

具有HollingⅡ型功能反应的捕-食模型的定性分析及最优收获策略

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.     

基于食饵保护的食饵-捕食捕鱼模型分析(英文)

In this paper,we consider a prey-predator fishery model with prey dispersal in a two-patch environment,one is assumed to be a free fishing zone and the other is a reserved zone where fishing and other extractive activities are prohibited.The existence of possible steady states of the system is discussed.The local and global stability analysis has been carried out.An optimal harvesting policy is given using Pontryagin s maximum principle.     

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.     

Coexistence in a discrete competition model with dispersal

We propose a discrete-time competition model between two populations to study the effects of dispersal upon population interactions. It is assumed that dispersal occurs after reproduction and in synchrony. We first analyse a two-patch single species population model with no interspecific competition. Based on these results, we derive sufficient conditions for population coexistence. It is proved that the system is uniformly persistent and possesses a unique coexisting equilibrium.     

改进了的捕食者-食饵系统的征税模型分析

探讨了Holling功能性反应的捕食者-食饵征税模型,修改了更合理的捕获函数.讨论了该系统生物经济平衡点的性态,正平衡点的局部渐近稳定性和全局渐近稳定性条件,并利用Pontrjagin最大值原理得到了最优税收策略.为可再生资源的合理开发利用提供了理论依据.     

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.     

具有阶段结构和时滞的捕食系统

§ 1　IntroductionThe competitive,cooperative and predator-prey models have been studied by many au-thors.[1— 4] The permanence (or strong persistence) and extinction are significant conceptsof those models.However,the stage structure of species has been considered very little.Inthe real world,almost all animals have the stage structure of immature and mature.Re-cently,papers[5— 7] studied the stage structure of species,the transformation rate of ma-ture population is proportional to the ex…     

一类带时滞的阶段结构捕食模型的定性分析

研究了一类具有时滞和阶段结构的捕食模型系统,给出了系统持续生存的充分条件.利用比较定理和构造适当的Lyapunov泛函得到了该系统正平衡态全局渐近稳定的充分条件.     

ON GLOBAL ASYMPTOTIC STABILITY OF THE ZERO SOLUTION OF A GENERALIZED LIENARD′S SYSTEM

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GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.     

阶段结构远海-近海渔业模型的稳定性及最优收获

§ 1　IntroductionAlong with the development of science and technology,the capacity and output offishing have increased.For example,in China,traditional and backward manual tools areused and the inshore coastlines are limited for fishing,but now gradual improvements inthe technical efficiency of fishing gear and vessels have radically changed the fishing sce-nario.With the advent of sophisticated fishing instruments,the fishing scope has been ex-panded from inshore area to offshore area.As a …     

具有时滞和基于比率的三种群捕食系统的持久性与全局渐近稳定性

研究一类具有时滞和基于比率的三种群食物链捕食-被捕食动力学模型.证明了该系统在适当条件下的一致持久性;通过构造Lyapunov泛函,得到了该系统正平衡点全局渐近稳定的充分条件.     

On the Construction of Globally Asymptotically Stable Liapunov Functions of a Type of Third－order Systems with Nonseparable Variables

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关于扰动微分方程零解稳定性若干定理的改进

本文运用Ляиунов第二方法研究扰动微分方程零解稳定性，分别研讨了所给扰动微分方程的局部稳定性、全局渐近稳定性以及全局一致渐近稳定性问题，得到若干定理，这些结果在一定条件下改进了文[1]的相应结果，运用更加广泛．