具有状态反馈脉冲控制的害虫管理SI模型的动力学性质

考虑到过量使用农药对环境和农作物造成的危害,文章提出了一类具有状态脉冲反馈控制策略的害虫管理SI控制模型,即,当易感害虫的数量到达经济危害水平时,施加生物和化学控制策略(例如,释放染病害虫且按易感害虫的比例喷洒杀虫剂),使得易感害虫的数量在极短的时间内低于危害阈值,从而达到控制病虫害的目的.通过使用微分几何理论,Poincaré映射,不动点定理等方法和技巧,建立了该控制模型系统正周期解存在性和稳定性的判别准则.     

一类状态依赖脉冲控制的害虫管理数学模型研究

研究一类状态依赖脉冲控制的害虫管理数学模型,当害虫的数量达到一定的临界值时,通过释放天敌和喷洒农药使得害虫的数量不超过经济危害水平.首先利用几何分析和后继函数方法得到了系统阶1周期解的存在性,进而运用类Poincare准则证明系统阶1周期解是轨道渐近稳定的.结论表明在一定的条件下,总能将害虫控制在经济危害水平以内,从而人们在农业生产过程中能够获得最大收益.证明系统存在阶1周期解的方法可推广到其它状态依赖脉冲反馈模型中.     

具非线性传染率与生物化学控制的害虫管理S-I模型

讨论了具有非线性传染率与脉冲控制的害虫管理S-I传染病模型,此模型考虑的是脉冲投放病虫和喷洒农药.不但得到了系统的所有解的一致完全有界,而且得到了害虫灭绝的边界周期解的全局渐进稳定和系统的一致持久的条件.为实际的害虫管理提供了可靠的理论依据.     

非线性脉冲状态依赖捕食-被捕食模型的定性分析

由于资源的有限性以及害虫群体对杀虫剂的抗性发展等因素,使得杀虫剂对害虫的杀死率具有饱和效应．因此,当害虫的数量达到经济阈值时, 杀虫剂对害虫的杀死率与经济阈值有关．为了刻画上述饱和效应,建立了一类非线性脉冲状态依赖捕食被捕食模型．利用Lambert W函数和脉冲半动力系统的相关技巧,分析了模型阶1正周期解的存在性和稳定性, 得到了相应的充分条件．进而讨论了非线性脉冲与线性脉冲对阶1周期解存在性的影响.     

基于虚拟变形法的供水管网漏损定位方法

针对供水管网的漏损探测与定位问题,采用虚拟变形法对管网各参数进行计算,通过漏损影响矩阵和流量影响矩阵来表征管网的状态,并提出了漏损探测定位的优化计算模型.由于管网漏损点数量事先难以预先获取,提出了基于贝叶斯理论的管网漏损探测、定位模型,并结合Matlab和Epanet编制了相应的优化计算程序,数值仿真结果验证了方法的有效性和可行性.     

具有反馈性能的传染病传播模型

传染病是人类社会面对的严重威胁之一,也是困扰世界医学界的长期难题.文中首先对传染病的传播机理进行了分析研究,将其传播分为自然传播和人为控制两种状态,然后以微分方程理论为基础,运用反馈控制理论分别建立了自然传播状态的闭环自激正反馈微分方程模型和有人为控制时的闭环负反馈微分方程模型,并引入控制度概念把上述两种反馈模型结合起来以反映人为控制因素对传染病传播系统的影响,最后以2003年爆发的SARS为例采用计算机编程仿真,结果与实际比较吻合,并提出了应对传染病的若干对策,为传染病的传播预测、有效预防和控制提供了一定的理论依据.     

害虫治理的病毒感染模型

研究了食饵受病毒感染且捕食者具有Beddington-DeAngelis功能性反应的生态流行病模型,此模型考虑的是脉冲释放病毒颗粒和自然天敌. 利用Floquet乘子理论、小振幅扰动技巧和比较定理证明了害虫根除周期解的全局渐近稳定性以及系统持续生存的充分条件.结论为现实的害虫管理提供了有效的策略依据.     

利用捕捉与再捕捉模型估计害虫发生量

森林害虫严重地危害着林木生长,如何及时有效地对害虫进行预测预报,林业工作者作了大量的研究,建立了许多害虫发生量的预测预报模型,并将其用于生产实际.但大都侧重于害虫发生量与气象、生态等因子关系的研究,是基于长期积累的气象、生态等因子和害虫发生的资料来建立模型预估的,而以某时某地的虫害情况来估计此时此地的害虫发生量,并建立模型的却很少,特别是捕捉与再捕捉模型(Darroch,1958)的应用几乎没有.在国外大部分仅用于鸟类和鱼类种群总量的估计,在森林害虫发生量的预估方面的报导也未见面.因此,我们首次将捕捉与再捕捉模型应用于森…     

森林火灾SIR模型及仿真模拟

本文借鉴传染病研究中的SIR模型,并结合森林火灾发生的特点,建立森林火灾SIR模型并对森林火灾燃烧扩散状态进行仿真模拟,根据模拟仿真结果及分析结论,得出了有效预防和控制森林火灾的手段.     

基于演化博弈理论的知识服务网络复制动态模型

在知识服务网络中,知识供应方和知识需求方在传递知识的过程中进行着重复博弈,并根据收益矩阵选择有利策略逐渐模仿,最终采用某个策略达到了演化稳定均衡状态.首先,根据演化博弈理论,建立了知识服务网络的复制动态演化博弈模型.然后,采用多智能体建模仿真方法及Netlogo仿真平台对所建模型进行仿真分析.最后,通过仿真分析得到在不同的初始情况下,知识主体最终的演化稳定策略与各主体中采取合作策略的初始比例和鞍点的大小关系有关,验证了所建立模型的正确性.     

The dynamics of pest control pollution model with age structure and time delay

In this paper, by using pollution model and impulsive delay differential equation, we investigate the dynamics of a pest control model with age structure for pest by introducing a constant periodic pesticide input and releasing natural enemies at different fixed moment. We assume only the pests are affected by pesticide. We show that there exists a global attractive pest-extinction periodic solution when the periodic natural enemies release amount μ₁ and pesticide input amount μ₂ are larger than some critical value. Further, the condition for the permanence of the system is also given. By numerical analyses, we also show that constant maturation time delay, pulse pesticide input and pulse releasing of the natural enemies can bring obvious effects on the dynamics of system. We believe that the results will provide reliable tactic basis for the practical pest management.     

Dynamics on a pest management SI model with control strategies of different frequencies

Based on spraying pesticide and introducing infected pest and natural enemy for pest control, an SI ecological epidemic model with different frequencies of pesticide applications and infected pests and natural enemy releases is proposed and studied. With spraying either more or less frequently than the releases, the threshold condition of existence and global attractiveness of susceptible pest extinction periodic solution is obtained. We investigate the effects of the pest control tactics on the threshold conditions. We also show that the system has rich dynamics including period-doubling bifurcations and chaos as the release period increases, which implies that the presence of impulsive intervention makes the dynamic behavior more complex. Finally, to see how the pesticide applications can be reduced, we develop a model involving periodic releases of natural enemies with chemical control applied only when the densities of the pest reaches the given Economic Threshold. It indicates that the hybrid method is the most effective method to control pest and the frequency of pesticide applications largely depends on the initial densities and the control tactics.     

Effects of population dispersal and impulsive control tactics on pest management

In this paper, we firstly consider a Lotka–Volterra predator–prey model with impulsive constant releasing for natural enemies and a proportion of killing or catching pests at fixed moments, and we have proved that there exists a pest-eradication periodic solution which is globally asymptotically stable. Further, we extend the model for the population to move in a two-patch environment. The effects of population dispersal and impulsive control tactics are investigated, i.e. we chiefly address the question of whether population dispersal is beneficial or detrimental for pest persistence. To do this, some special cases are theoretically investigated and numerical investigations are done for general case. The results indicate that for some ranges of dispersal rates, population dispersal is beneficial to pest control, but for other ranges, it is harmful. These clarify that we can get some new effective pest control strategies by controlling the dispersal rates of pests and natural enemies.     

Impulsive adult culling of a tropical pest with a stage-structured life cycle

We recognise that many pests, especially insects, lead a stage-structured life cycle. This leads us to formulate three population models for a pest with a life cycle of two stages, namely juvenile and adult. The birth function is different for each model — we consider linear, Nicholson, and Allee birth functions. Aware of the fact that adult insects may be driven into the open by an instinct to mate, we decide to implement an impulsive adult culling regime to control the pest. Since applying pesticides is potentially unwise if the pest will die out naturally, we first find natural extinction and endemicity results and only then construct a successful culling regime for implementation in the event of natural endemicity. Of particular significance is the calculation of an explicit finite upper bound for the number of culls needed to guarantee extinction in the Allee model. But a simulation for the Nicholson model reveals as well that infrequent culling can make a pest more successful than in the absence of culling. Finally we discuss the advantages and disadvantages of large-scale applications of pesticides and urge that care be taken in making decisions to apply them.     

MODELING INVASION OF PESTS RESISTANT TO Bt TOXINS PRODUCED BY GENETICALLY MODIFIED PLANTS: RECESSIVE VS. DOMINANT INVADERS

ABSTRACT. There is a growing public concern about the ecological and evolutionary consequence of the use of genetically modified organisms. We study the impact of Bt resistant pests on genetically modified Bt crops and compare exposure of Bt plants to recessive and dominant Bt resistant invaders. To simulate pest invasion we develop a conceptual reaction‐diffusion model of the Bt crop Bt susceptible insects Bt resistant insects for both the recessive and dominant pests. We show by means of computer simulations that there is a key parameter which we define as the growth number that characterizes the insects' fitness. We also show that the Bt resistant insects' invasion can lead to inhomogeneity in plant and insect spatial distributions. The plant and insect spatial patterns resulting from the Bt resistant insects' invasion are found to be dependent on the duration of the Bt resistant insect reproduction period. We compare averaged plant biomass resulting from the invasion of the dominant insects with the averaged plant biomass resulting from the invasion of the recessive insects. As a result, we show that in contrast to the recessive insects, the dominant ones initiate destruction of the plant population if the inflow of Bt susceptible insects is more than a critical value. In this case the plant biomass decays to zero. Otherwise, the plant biomass under the invasion of both the dominant and recessive insects depends on the duration of the insect reproduction period. We conclude that under invasion of dominant Bt resistant pests, the refuge strategy which has received wide acceptance in agricultural practice may not be scientifically sound practice.     

Modelling and analysis of an impulsive SI model with Monod-Haldane functional response

An impulsive SI model with Monod-Haldane functional response for pest control is proposed and investigated. First, we have proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the above system can be permanent. Then, influences of impulsive perturbation including impulse period, the time of spraying pesticide and the quantity of releasing infective pests on the above system have been studied. Moreover, numerical simulations show that the system has rich dynamical behaviors. Finally, it is concluded that the approach of combining impulsive infective releasing with impulsive pesticide spraying is more effective than the classical one if the chemical control is adopted rationally.     

Optimal threshold density in a stochastic resource management model with pulse intervention

Human activities and agricultural practices are having huge impacts on the development of fishery and land resources through different ways. To model such systems that involve harvesting, an impulsive model of natural resources with a stochastic noise perturbation element is formulated to study the relationship between (a) the maximal expectation of biomass after harvesting or fishing events and (b) the minimal expectation of pest biomass and the number of times pesticide is applied. Using a detailed analytical treatment, time estimation, and numerical demonstrations, we establish that the proposed mechanism is capable of maximizing fish populations at the end of a fishing season and minimizing pest numbers after a crop harvesting season once the intensity of the noise is relatively small. Investigations of the effects of different parameters reveal that theoretical predictions from the new stochastic model accord with those from the deterministic case. Recommendations for Resource Managers

• Various measures can be implemented to manage natural resources, such as adjusting fishing quantity and intensity to maximize fish population.
• In the natural environment, population growth is inevitably affected by the environment noise. So it is important to understand the noise effect to maintain sustainability of resources.
• Investigated methods are useful to converse resources and can be widely applied to control pests.

     

Models for determining how many natural enemies to release inoculatively in combinations of biological and chemical control with pesticide resistance

Combining biological and chemical control has been an efficient strategy to combat the evolution of pesticide resistance. Continuous releases of natural enemies could reduce the impact of a pesticide on them and the number to be released should be adapted to the development of pesticide resistance. To provide some insights towards this adaptation strategy, we developed a novel pest–natural enemy model considering both resistance development and inoculative releases of natural enemies. Three releasing functions which ensure the extinction of the pest population are proposed and their corresponding threshold conditions obtained. Aiming to eradicate the pest population, an analytic formula for the number of natural enemies to be released was obtained for each of the three different releasing functions, with emphasis on their biological implications. The results can assist in the design of appropriate control strategies and decision-making in pest management.     

An integrated pest management model with delayed responses to pesticide applications and its threshold dynamics

Pulse-like pest management actions such as spraying pesticides and killing a pest instantly and the release of natural enemies at critical times can be modelled with impulsive differential equations. In practice, many pesticides have long-term residual effects and, also, both pest and natural enemy populations may have delayed responses to pesticide applications. In order to evaluate the effects of the duration of the residual effectiveness of pesticides and of delayed responses to pesticides on a pest management strategy, we developed novel mathematical models. These combine piecewise-continuous periodic functions for chemical control with pulse actions for releasing natural enemies in terms of fixed pulse-type actions and unfixed pulse-type actions. For the fixed pulse-type model, the stability threshold conditions for the pest eradication periodic solution and permanence of the model are derived, and the effects of key parameters including killing efficiency rate, decay rate, delayed response rate, number of pesticide applications and number of natural enemy releases on the threshold values are discussed in detail. The results indicate that there exists an optimal releasing period or an optimal number of pesticide applications which maximizes the threshold value. For unfixed pulse-type models, the effects of the killing efficiency rate, decay rate and delayed response rate on the pest outbreak period, and the frequency of control actions are also investigated numerically.     

The onset of positive periodic solutions for a biochemical pest management model

In this paper, the bifurcation of nontrivial periodic solutions for an impulsively perturbed system of ordinary differential equations which models an integrated pest management strategy is studied by means of a fixed point approach. A biological control, consisting in the periodic release of infective pests, and a chemical control, consisting in pesticide spraying, are employed to maintain susceptible pests below an acceptable level. It is assumed that the biological and chemical control act with the same periodicity, but not in the same time. It is then shown that if the constant amount of infective pests released each time reaches a certain threshold value, then the trivial susceptible pest-eradication periodic solution loses its stability, which is transferred to a newly emerging nontrivial periodic solution.