具时滞和脉冲的捕食者-食饵模型的动力学性质

基于害虫的生物控制和化学控制策略,考虑到化学杀虫剂对天敌的影响,利用脉冲微分方程建立了在不同的固定时刻分别喷洒杀虫剂和释放天敌的具有时滞的第III功能反应的捕食者-食饵脉冲动力系统.证明了当脉冲周期小于某个临界值时,系统存在一个渐进稳定的害虫灭绝周期解,否则系统持续生存.并用Matlab软件对害虫灭绝周期解及害虫周期爆发现象进行了数值模拟.     

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.     

基于喷洒杀虫剂及释放病虫的脉冲控制害虫模型

基于喷洒杀虫剂及释放病虫的综合控制害虫策略,建立了具有脉冲控制的微分方程模型.利用脉冲微分方程的F loquet理论、比较定理,证明了害虫灭绝周期解的全局渐近稳定性与系统的持久性.     

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.     

基于脉冲控制的害虫管理数学模型研究

研究一类害虫管理SI传染病模型,考虑脉冲投放病虫和人工捕杀相结合,得到系统的灭绝周期解,给出此周期解的全局吸引性,并获得了系统一致持续生存的条件.给出了害虫管理综合防治策略.     

基于IPM策略和食物助增捕食者的捕食系统

研究了综合害虫治理(IPM)策略下具有脉冲作用和食物助增捕食者种群的捕食系统.得到了害虫灭绝周期解全局渐近稳定和系统持续生存的条件.     

具有Monod-Haldane功能反应和脉冲效应的捕食系统的动力学性质

基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件．并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟．     

污染环境下具有脉冲输入环境毒素的单种群模型的灭绝阈值研究

本文研究了污染环境下具脉冲输入环境毒素的单种群模型.利用乘子理论和小振幅扰动法,当脉冲周期小于一个临界值时,我们得到了种群灭绝周期解是全局渐近稳定的,同时我们还得到了种群持久的条件.从生物学的观点看,污染环境下保护物种的方法是控制环境毒素的排放周期或排放量.我们的结论为资源环境下的生物资源管理提供了策略基础.     

一类具有脉冲控制的害虫管理SI数学模型研究

研究一类具有脉冲控制的害虫管理SI数学模型,运用Floquet理论证明了系统害虫灭绝周期解的全局渐近稳定性,并对所得结论进行了数值模拟.     

捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型

讨论了与害虫治理相关的一类捕食者具脉冲扰动与食饵具有化学控制的阶段结构时滞捕食-食饵模型,得到了害虫灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.得出的结论为现实的害虫治理提供了可靠的策略依据.     

Dynamic analysis of a pest management SEI model with saturation incidence concerning impulsive control strategy

According to biological strategy for pest control, we investigate the dynamic behavior of a pest management SEI model with saturation incidence concerning impulsive control strategy-periodic releasing infected pests at fixed times. We prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. When the impulsive period is larger than some critical value, the stability of the pest-eradication periodic solution is lost; the system is uniformly permanent. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels. Numerical results show that the system we consider can take on various kinds of periodic fluctuations and several types of attractor coexistence and is dominated by period-doubling cascade, symmetry-breaking pitchfork bifurcation, quasi-periodic oscillate, chaos, and non-unique dynamics.     

The dynamics of an epidemic model for pest control with impulsive effect

In pest control, there are only a few papers on mathematical models of the dynamics of microbial diseases. In this paper a model concerning biologically-based impulsive control strategy for pest control is formulated and analyzed. The paper shows that there exists a globally stable susceptible pest eradication periodic solution when the impulsive period is less than some critical value. Further, the conditions for the permanence of the system are given. In addition, there exists a unique positive periodic solution via bifurcation theory, which implies both the susceptible pest and the infective pest populations oscillate with a positive amplitude. In this case, the susceptible pest population is infected to the maximum extent while the infective pest population has little effect on the crops. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamic, which implies that this model has more complex dynamics, including period-doubling bifurcation, chaos and strange attractors.     

Extinction and permanence of a two-prey two-predator system with impulsive on the predator

In this paper, the dynamic behaviors of a two-prey two-predator system with impulsive effect on the predator of fixed moment are investigated. By applying the Floquet theory of liner periodic impulsive equation, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we prove that the system is permanent if the impulsive period is large than some critical value, and meanwhile the conditions for the extinction of one of the two prey and permanence of the remaining three species are given. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels.     

A Holling II functional response food chain model with impulsive perturbations

In this paper, we investigate a three trophic level food chain system with Holling II functional responses and periodic constant impulsive perturbations of top predator. Conditions for extinction of predator as a pest are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of predator eradication periodic solution. Further, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which shows the rich dynamics (for example: period doubling, period halfing, chaos crisis) in the positive octant. The dynamics behavior is found to be very sensitive to the parameter values and initial value.     

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.     

Dynamic analysis of pest control model with population dispersal in two patches and impulsive effect

In this paper, we investigate the pest control model with population dispersal in two patches and impulsive effect. By exploiting the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we can obtain that the susceptible pest eradication periodic solution is globally asymptotically stable if the impulsive periodic τ is less than the critical value τ₀ . Further, we also prove that the system is permanent when the impulsive periodic τ is larger than the critical value τ₀. Hence, in order to drive the susceptible pest to extinction, we can take impulsive control strategy such that τ < τ₀ according to the effect of the viruses on the environment and the cost of the releasing pest infected in a laboratory. Finally, numerical simulations validate the obtained theoretical results for the pest control model with population dispersal in two patches and impulsive effect.     

The Dynamics of a Prey-dependent Consumption Model Concerning Integrated Pest Management

A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey-dependent consumption concerning integrated pest management are very complex, including period-doubling cascades, chaotic bands with periodic windows, crises, symmetry-breaking bifurcations and supertransients.     

Analysis of a predator–prey model with Holling II functional response concerning impulsive control strategy

According to biological and chemical control strategy for pest control, we investigate the dynamic behavior of a Holling II functional response predator–prey system concerning impulsive control strategy-periodic releasing natural enemies and spraying pesticide at different fixed times. By using Floquet theorem and small amplitude perturbation method, we prove that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, the condition for the permanence of the system is also given. Numerical results show that the system we consider can take on various kinds of periodic fluctuations and several types of attractor coexistence and is dominated by periodic, quasiperiodic and chaotic solutions, which implies that the presence of pulses makes the dynamic behavior more complex. Finally, we conclude that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently.     

A delayed epidemic model with stage-structure and pulses for pest management strategy

From a biological pest management standpoint, epidemic diseases models have become important tools in control of pest populations. This paper deals with an impulsive delay epidemic disease model with stage-structure and a general form of the incidence rate concerning pest control strategy, in which the pest population is subdivided into three subgroups: pest eggs, susceptible pests, infectious pests that do not attack crops. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic susceptible pest-eradication solution of the system and observe that the susceptible pest-eradication periodic solution is globally attractive, provided that the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than another critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its attractivity. Our results indicate that besides the release amount of infective pests, the incidence rate, time delay and impulsive period can have great effects on the dynamics of our system.