带脉冲和时滞影响的非线性双曲型方程振动性的新准则

考虑一类具非线性扩散项的脉冲时滞双曲型偏微分方程的振动性,借助一阶脉冲时滞微分不等式,获得了该类方程在Dirichlet边值条件下所有解振动的若干充分判据.     

具非线性扩散项的脉冲抛物方程的强迫振动性

研究一类具非线性扩散项的脉冲抛物型方程解的强迫振动性问题,借助平均技巧和脉冲微分不等式,建立了该类方程在Dirichlet边值条件下所有解强迫振动的若干新的充分判据.结论充分表明振动是由脉冲效应引起的.     

带非线性扩散项的脉冲时滞抛物方程的振动性与渐近性

研究一类带非线性扩散项的脉冲时滞抛物方程在Dirichlet边值条件下的振动性问题,借助脉冲时滞微分不等式,建立了该类方程一切解u(x,t)振动或者limt→+∞∫Ωu(x,t)dx=0的若干新的充分性判据.     

具有非局部对流一类反应扩散方程脉冲解存在性

该文讨论具有非局部对流的一类反应扩散方程的脉冲解的存在性借助于方程的某种对称性，利用三维空间中追赶法技巧及拓扑方法，当参数ε在一定范围内，证明了方程的脉冲解存在性．最后给出波速Ｃ与人口速率和出生及死亡的动力学过程的相互关系．     

具扩散的年龄结构脉冲随机时滞种群方程的均方稳定性(英文)

本文考虑一类具扩散的年龄结构脉冲随机时滞种群方程.主要目的是研究具扩散的年龄结构脉冲随机时滞种群平凡解的均方稳定性,给定两个使平凡解均方稳定的充分条件.     

竞争型反应扩散方程的正解与时间最优控制

本文研究了一类竞争型反应扩散方程的时间最优控制问题的存在性问题.利用上下解的方法,得到了反应扩散方程正解的存在性.利用Kakutani不动点定理,证明了反应扩散方程关于正轨迹的局部精确能控性,并据此证明了时间最优控制的存在性.     

脉冲Logistic方程的正周期解

先证明具有脉冲 Logistic方程的正周期解存在的充要条件和吸引性 ,然后讨论具有脉冲和时滞的 L ogistic方程的正周期解存在性 ,推广了相应的结论 .     

带有非局部扩散的反应流动扩散方程的行波解

本文主要考虑带有非局部扩散项的反应流动扩散方程行波解的存在性问题.首先,利用Schauder不动点定理和上下解原理得到带有非局部扩散项的反应流动扩散方程行波解的存在性,再将所得的结论应用到带有流动项的Lotka-Volterra竞争模型上,最后,考虑了流动项对繁殖速度的影响.同时,本文得到的存在性结论可以应用到一般的反应流动扩散方程中.     

具脉冲时滞的Duffing型方程的周期解

利用Mawhin重合度理论,研究了脉冲时滞Duffing型方程的周期解的存在性.本 文结果即使对相应的非脉冲Duffing型方程也是新的.     

具脉冲和时滞影响的非线性抛物系统边值问题的振动结果

研究一类具非线性扩散项的脉冲时滞抛物偏微分系统解的振动性,借助Green公式、垂直相加法和脉冲时滞微分不等式,获得了该类系统在Robin边值条件下振动的充分性条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

Dynamics behaviors of a delayed stage-structured predator-prey model with impulsive effect

In this paper, we analyzed a delayed stage-structured predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions for the global attractivity of ‘predator-eradication’ periodic solution and permanence of the system are obtained. The results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system.     

具有脉冲效应的害虫管理系统的灭绝性与持续性

研究一类具有脉冲效应的害虫管理系统,讨论了系统的灭绝性和持续性,给出了系统灭绝和持续生存的阈值条件,并对所得结论进行了数值模拟.     

Permanence for General Nonautonomous Impulsive Population Systems of Functional Differential Equations and Its Applications

In this paper, we investigate general impulsive nonautonomous population dynamical systems of functional differential equations. By utilizing the method of multiple Liapunov-like functionals to construct the permanence region, a general criterion on the permanence for the system is established. Furthermore, as applications of this general criterion, a class of impulsive nonautonomous n-species Lotka–Volterra competitive systems with delays and a class of impulsive nonautonomous 3-species Lotka–Volterra food chain systems with delays are discussed. Some new and useful sufficient conditions on the permanence for these systems are established.     

具有非单调功能反应和脉冲扰动的捕食系统的分析

研究捕食者具有非单调功能反应和周期脉冲扰动的食饵-捕食系统,利用脉冲微分方程的F loquet理论和比较定理,得到了系统灭绝和持续生存的充分条件.     

具有Holling Ⅲ功能反应和阶段结构的Gompertz生态系统的持久性

以生态学与微分方程的理论和方法为基础,建立了一类具有HollingⅢ功能反应和阶段结构的生态Gompertz模型.利用频闪映射,获得了捕食者灭绝周期解,分析了此周期解的全局吸引性.在对食饵进行脉冲收获和捕食者具有成长期时滞条件下,运用脉冲微分方程比较定理和小振幅扰动技巧,获得了系统一致持续生存的条件.     

Threshold dynamics of a stage-structured single population model with non-transient and transient impulsive effects

In this paper, we present a stage-structured single population model with non-transient and transient impulsive effects. By the stroboscopic map theories of impulsive differential equations, we obtain the sufficient conditions for the permanence of the investigated system. The results indicate that the thresholds of the transient impulsive harvesting amount and the non-transient impulsive harvesting interval play important roles on the permanence of population. Our results also provide reliable tactic basis for the practical biological resource management.     

具有非单调功能反应和脉冲扰动的捕食系统的研究

研究捕食者具有非单调功能反应和周期脉冲扰动的捕食者一食饵系统，利用脉冲微分方程的Floquet理论和比较定理，得到了系统灭绝和持续生存的充分条件．最后，通过数值模拟阐明系统在周期脉冲扰动下的复杂性．     

一类具部分依赖和脉冲作用的捕食系统

分析了一类具部分依赖和脉冲作用的捕食系统,得到了食饵灭绝周期解局部稳定和系统持续生存条件.     

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.     

Permanence in a periodic single species system subject to linear/constant impulsive perturbations

In this paper, a single species system with linear/constant impulsive perturbations is established. The linear and constant impulses are realized at fixed moments of time. By using the comparison principle of impulsive differential equations and analysis techniques, sufficient conditions for the permanence of the system with linear and constant impulsive perturbations are obtained, respectively. Numerical simulations are presented to substantiate our analytical results, and show that the impulsive perturbations play a crucial role. Copyright © 2010 John Wiley & Sons, Ltd.