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.     

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.     

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.     

一个具有时滞和功能反应的非自治阶段结构的捕食模型

研究一个具有时滞和功能反应的非自治阶段结构的捕食模型,其中食饵种群分两个阶段——幼年和成年,且捕食种群只捕成年食饵.通过利用微分不等式、比较定理和构造适当的Lyapunov泛函,得到该模型的永久持续生存和绝灭的充分条件,同时也得到了周期系统存在唯一全局渐近稳定的周期解的充分条件.     

一类具有一般出生函数阶段结构的传染病模型的全局分析

假设种群个体生长分幼年和成年两个阶段以及疾病仅在成年阶段传播,建立并研究了一类幼年个体输入率为一般函数的传染病模型,得到了决定种群存活与否的种群存活基本再生数和决定疾病传播灭绝与否的疾病传播基本再生数,通过构造适当的Lyapunov函数分析了模型的全局阈值动力学性态.     

具有Beddington-DeAngelis型功能反应函数的阶段结构捕食-食饵模型

讨论了捕食者和食饵都具有阶段结构的捕食食饵模型.考虑到捕食者梭皮龟捕获食饵水母时彼此之间的干扰效应,用到了Beddington-DeAngelis型功能反应函数,食饵水母的幼年为水螅体,捕食者梭皮龟仅以成年水母为食.运用渐近系统理论得到了模型边界平衡点的全局渐近稳定性,运用一致持久生存理论得到了捕食者的一致持久性.最后,运用数值模拟的方式不仅验证了定性理论分析的结果,同时显示了捕食者之间适当的干扰可以有效控制水母种群的数量.     

具有阶段结构的SIR传染病模型

研究了一类具有阶段结构的SIR传染病模型，在模型中假设种群分幼年和成年两个阶段，且只有成年种群染病，并且采用与成年易感者数量有关的一般非线性传染率，得到了系统解的有界性及无病平衡点和地方病平衡点存在的条件．通过对平衡点对应的特征方程的讨论得到了平衡点局部渐近稳定的条件，同时证明了平衡点的全局渐近稳定性，并对结论进行了数值模拟．     

具两系统切换的脉冲阶段结构单种群动力学模型研究

建立具两系统切换脉冲阶段结构单种群动力学模型,利用离散动力系统频闪映射理论,得到系统种群灭绝与系统种群持续生存的控制阈值.结果表明脉冲收获与冬眠期对于系统种群持久起着重要作用,从而为现实的生物资源管理与生物多样性保护提供了可靠的策略依据.     

具脉冲效应的阶段结构单种群动力学模型

讨论了生物资源管理中的具脉冲出生与脉冲收获的单种群阶段结构动力学模型.利用离散动力系统频闪映射理论,得到了脉冲投放幼体对整个种群持续生存的重要意义.为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲微分方程理论.     

毒素脉冲输入与种群脉冲出生切换阶段结构单种群动力学模型研究

本文研究了毒素脉冲输入与脉冲出生切换阶段结构单种群动力学模型.利用常微分方程及差分分析,获得了系统种群灭绝和持久生存的控制条件结果,为污染环境中的生物资源管理提供了可靠的管理策略.     

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.     

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.     

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.     

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.     

Homoclinic bifurcation for a general state-dependent Kolmogorov type predator–prey model with harvesting

In this paper, a general Kolmogorov type predator–prey model is considered. Together with a constant-yield predator harvesting, the state dependent feedback control strategies which take into account the impulsive harvesting on predators as well as the impulsive stocking on the prey are incorporated in the process of population interactions. We firstly study the existence of an order-1 homoclinic cycle for the system. It is shown that an order-1 positive periodic solution bifurcates from the order-1 homoclinic cycle through a homoclinic bifurcation as the impulsive predator harvesting rate crosses some critical value. The uniqueness and stability of the order-1 positive periodic solution are derived by applying the geometry theory of differential equations and the method of successor function. Finally, some numerical examples are provided to illustrate the main results. These results indicate that careful management of resources and harvesting policies is required in the applied conservation and renewable resource contexts.     

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.     

Single impulsive controller for globally exponential synchronization of dynamical networks

This paper is devoted to studying the synchronization control of impulsive dynamical networks. A single impulsive controller is proved to be effective for the stabilization of dynamical networks with impulse-coupling. Some simple and easily verified criteria are given for the stabilization of impulsive dynamical networks under a single impulsive controller and/or a single negative state-feedback control. Moreover, the effects of a single impulsive controller, a single state-feedback controller and an isolated dynamical system on the synchronization process are respectively distilled and explicitly expressed in the derived criteria. The structure of the dynamical network can be directed and weakly connected with a rooted spanning tree. Moreover, the convergence rate of the dynamical network is also explicitly estimated, and there is no requirement on the lower and upper bounds of the impulsive intervals. A numerical example is presented to illustrate the efficiency of the designed controller and the validity of the analytical results.