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.     

脉冲输入免疫因子的HBV模型的稳定性和持久性分析

提出了一个数学模型,用于研究脉冲投放免疫因子对HBV传染病动力学的影响.通过利用脉冲微分不等式和比较定理,证明了HBV模型的无病周期解的存在性,给出了无病周期解的全局渐近稳定性和系统的持续性的充分条件.研究结果表明:短的投放周期或适当的免疫因子投放量可以导致HBV的清除.     

脉冲输入免疫因子的HBV模型的稳定性和持久性分析

提出了一个数学模型,用于研究脉冲投放免疫因子对HBV传染病动力学的影响.通过利用脉冲微分不等式和比较定理,证明了HBV模型的无病周期解的存在性,给出了无病周期解的全局渐近稳定性和系统的持续性的充分条件.研究结果表明:短的投放周期或适当的免疫因子投放量可以导致HBV的清除.     

一类带有功能性反应和脉冲效应的捕食系统的动力学性质

本文讨论了一类带有HollingⅡ类功能性反应和脉冲投放的一食饵两捕食者系统.运用Floquet和小振幅扰动理论,证明了当投放周期小于某个临界值时,系统食饵绝灭的周期解是全局渐近稳定的,同时研究了系统的持续生存.     

具有脉冲效应的两食饵一捕食者系统分析

构建并分析了一个在固定时刻脉冲投放捕食者且具有功能性反应的两食饵一捕食者系统,应用脉冲比较定理和微分方程的分析方法,得到了食饵灭绝周期解稳定的条件和系统持续生存的条件,并数值分析了所得的理论结果.     

具有脉冲毒素投放和营养再生的恒化器模型

研究具有脉冲毒素投放和营养再生的恒化器模型.利用脉冲微分方程的比较定理和小扰动方法得到了边界周期解全局渐近稳定的充分条件,进而得到了系统持续生存的充分条件.结果表明毒素环境将会导致微生物种群的灭绝.     

生境修复对具有Monod-Haldane功能反应的食饵捕食者系统的影响分析

为研究生境修复对生态系统产生的影响,文章建立了一类在生境破坏情况下,具有Monod-Haldane功能反应,脉冲比例收获和脉冲常数投放的四种群食饵-捕食者模型.利用脉冲比较定理,Floquent理论及微小扰动法研究了系统的动力学性质,并给出系统中两食饵灭绝和种群持续生存的充分条件.最后,通过数值模拟验证了所得结论.结果显示系统存在一定脆弱性和复杂性,随着生境修复比率和捕食者投放比率的变化,系统将出现拟周期,混沌等复杂的动力学现象.环境修复作用对系统影响的复杂性,也体现了生境修复的重要性.     

一类具有不育和脉冲投放的捕食模型

建立了一类具有不育控制和脉冲投放的捕食模型.判断了食饵灭绝周期解存在和全局渐近稳定的充分条件,还得到了种群一致持续生存的充分条件.     

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.     

一类具有常数脉冲投放的三种群捕食系统

考虑了一类两食饵种群具有密度制约和常数脉冲投放的三种群捕食系统,证明了当无捕食者时系统存在一个正周期解,并讨论了这个正周期解的全局渐近稳定性及其条件.     

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.     

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.     

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.     

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.     

具有脉冲扰动和非单调功能反应的三种群捕食系统的分析

研究一类具有脉冲效应和非单调功能反应的两个捕食者一个食饵害虫控制系统．通过脉冲微分方程的Floquet理论和小幅扰动方法,证明了当脉冲周期小于某个临界值时,系统存在一个渐近稳定的害虫根除周期解,否则系统是持续生存的．最后,通过数值实例,给出了一简单讨论．     

A study on time-limited control of single-pest with stage-structure

Two kinds of time-limited pest control models of single-pest with stage-structure, which can be described by the boundary value problem of ordinary differential equation and impulsive differential equation, are presented according to the ways of artificial control (continuous control and impulsive control). The conditions under which the corresponding model has a solution are given. If the model has a solution, the corresponding aim of pest control can be achieved. The theoretical results show that both the mature and the immature pest should be controlled synchronously, otherwise the aims of pest control can not be achieved in a finite time. Finally, some discussions and numerical simulations show that the impulsive control is more practical than the continuous control.     

Complex Dynamics of an Impulsive Control System in which Predator Species Share a Common Prey

In an ecosystem, multiple predator species often share a common prey and the interactions between the predators are neutral. In view of this fact, we propose a three-species prey-predator system with the functional responses and impulsive controls to model the process of pest management. It is proved that the system has a locally stable pest-eradication periodic solution under the assumption that the impulsive period is less than some critical value. In particular, two single control strategies (biological control alone or chemical control alone) are proposed. Finally, we compare three pest control strategies and find that if we choose narrow-spectrum pesticides that are targeted to a specific pest’s life cycle to kill the pest, then the combined strategy is preferable. Numerical results show that our system has complex dynamics including period-doubling bifurcation, quasi-periodic oscillation, chaos, intermittency and crises. This work is supported by National Natural Science Foundation of China (10171106).     

Impulsive control for a predator-prey Gompertz system with stage structure

For pest control in agriculture, we investigate the dynamics of a stage-structured predator-prey Gompertz system with impulsive spraying pesticide and releasing of natural enemies at different fixed moment. Using the stroboscopic map and comparison theorem, we obtain the sufficient conditions for the global attractivity of the mature predator-extinction periodic solution and the permanence of the system. Numerical simulations are inserted to verify the feasibility of the theoretical results, which show that the impulsive control plays a key role on the permanence of the system and also provide tactical basis for pest control.     

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.     

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.