关于一类二次微分系统的概周期解及周期解（英文）

周期解及概周期解问题在生物科学和其他领域具有重要价值.探究一类二次微分系统的周期解及概周期解,分析了附有周期系数系统的周期解的存在性,证明了附有概周期系数系统的概周期解的存在唯一性及全局吸引性.     

一类中心型半连续动力系统的周期解

讨论了一类中心型半连续动力系统的阶1周期解和阶2周期解的存在性、个数及其稳定性,给出该中心型系统存在唯一、两个、无穷多个阶1周期解和阶2周期解的条件,并给出了相应理论结果的数值模拟.     

具年龄结构和时滞的自食种群系统的周期解

利用延拓定理讨论具年龄结构和时滞的自食种群系统正周期解的存在性,得到周期解存在的条件,推广了已有结论.     

具周期脉冲的周期差分系统的全局性态

本文建立了具有常数脉冲和周期脉冲的周期差分系统,得到了常数脉冲系统全局稳定周期解存在的充分条件,并证明了周期脉冲的周期系统的周期解是全局吸引的。     

一类带参数的泛函微分方程的正周期解的存在性(英文)

利用锥上不动点理论,本文研究了一类非线性泛函微分方程正周期解的存在多样性和ω-周期解的不存在性.获得了一些新的结果.应用这些新的结果,讨论了一类带参数的血细胞生成模型,给出该模型的正周期解的存在性,此结果利用以前的方法是无法得到的.     

含有两个时滞项的退化时滞微分方程周期解

讨论了含有两个时滞项退化时滞微分方程的周期解的问题,特别的,给出了此类方程存在非常数周期解的充要条件,并对二维退化微分方程给出了非常数周期解存在性的代数判据,并在最后给出一个例子验证了判据的有效性.     

时标上具有HollingⅢ型功能反应的捕食模型的周期解

研究了时标上一类具有Holling型功能反应的捕食模型.运用时标上连续拓扑度定理,得到了系统存在周期解的充分条件,从而使系统的连续时间情形和离散时间情形的周期解问题得到了统一,该方法可广泛应用于研究微分方程和差分方程的周期解的存在问题.     

一类具有相互干扰的Leslie捕食与被捕食系统的定性分析

用定性分析的方法研究了一类具有相互干扰的Leslie捕食与被捕食周期系统的全局性质,讨论了系统的持久性以及周期解的存在唯一性,并且给出了该系统持久性的充分条件以及存在全局渐近稳定正周期解的充分条件.     

一类泛函微分方程的多重正周期解(英文)

联合运用Krasnoselskii不动点定理和Avery-Henderson不动点定理研究一类泛函微分方程的多重正周期解的存在性,获得了存在多重正周期解的充分条件.     

一类捕食-被捕食系统周期解的存在性

对于二维非自治捕食-被捕食系统,本文讨论了它的解的有界性,进而得到周期解和正周期解的存在性。     

Periodic solution of a chemostat model with Monod growth rate and impulsive state feedback control

In this paper, we develop a mathematical model concerning a chemostat with impulsive state feedback control to investigate the periodicity of bioprocess. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions under which the model has a periodic solution of order one are obtained. Furthermore, we estimate the position of the periodic solution of order one and discuss the existence of periodic solution of order two. The theoretical results and numerical simulations indicate that the chemostat system with impulsive state feedback control either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentrations of microorganisms and substrate.     

Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments.

In this paper, we study the existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems. By using the method of coincidence degree and Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution of periodic n-species Lotka-Volterra competition systems with several deviating arguments and the existence of a unique globally asymptotically stable periodic solution with strictly positive components of periodic n-species Lotka-Volterra competition system with several delays. Some new results are obtained. As an application, we also examine some special cases of the system we considered, which have been studied extensively in the literature. Some known results are improved and generalized.     

Global dynamics of an SIRS epidemic model with saturation incidence

In this paper, the dynamical behavior of an SIRS epidemic model with birth pulse, pulse vaccination, and saturation incidence is studied. By using a discrete map, the existence and stability of the infection-free periodic solution and the endemic periodic solution are investigated. The conditions required for the existence of supercritical bifurcation are derived. A threshold for a disease to be extinct or endemic is established. The Poincaré map and center manifold theorem are used to discuss flip bifurcation of the endemic periodic solution. Moreover, numerical simulations for bifurcation diagrams, phase portraits and periodic solutions, which are illustrated with an example, are in good agreement with the theoretical analysis.     

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour.     

扩散与时滞有关的单种群植物模型的全局稳定性

研究了具有周期系数及扩散与时滞有关的单种群植物模型,得到了该系统存在全局渐近稳定的正周期解的充分条件,其中该条件依赖时滞与扩散     

状态依赖脉冲微分方程的周期解的存在性及其在害虫治理中的应用

在文献[1]中研究的状态依赖脉冲微分方程的基础上,推广了其中的判定一般性平面自治状态依赖脉冲微分方程的准则,并利用它得到了文献[1]中所没有涉及到的情况下的状态依赖脉冲微分方程的阶一周期解☆栌在性．之后本文以此为基础并结合数值模拟的手段讨论了系统在农业害虫治理中的一些应用意义．     

具有时滞和基于比率的一类捕食者-食饵系统全局周期解的存在性

利用重合度理论研究一类具有时滞和基于比率的捕食者-食饵系统的全局周期解的存在性,得到了周期正解存在的充分条件。     

非自治阶段结构合作系统的持久性与周期解

本文研究一类非自治阶段结构的合作系统,得到系统的最终有界性,对应周期系统正周期解的存在性,唯一性以及全局渐近稳定性的充分条件。     

一类带时滞竞争模型的周期解

研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统．用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件．