时标上一捕食二食饵系统的周期解（英文）

研究时标上一捕食二食饵系统.运用时标上Gaines和Mawhin的连续拓扑度定理,得到了系统存在周期解的新的充分条件.其研究方法可以广泛地运用来研究微分或者差分方程的周期解存在性问题.     

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.     

高阶混合中立型差分方程的振动性质

研究了一类高阶混合中立型差分方程的振动性质,得到了这类差分方程的振动判据.     

一类食饵具有S-型变收获率的非自治离散捕食系统渐近行为

建立并研究了一类具有S-型变收获率的非自治离散捕食系统,应用差分不等式、Brouwer不动点定理和分析技巧分别建立了系统的持久生存性,正周期解的存在性及全局渐近稳定性的充分条件,我们还给出了具体验证例子及相应的数值模拟结果.     

离散时间的互惠系统的正周期解的存在性

利用重合度理论中的延拓定理研究了一类具有周期系数的离散时间的差分互惠系统模型．得到了该系统正周期解存在的充分条件．     

一类具有反馈控制的概周期时滞差分竞争系统（英文）

通过应用概周期函数壳理论和构造Lyapunov函数的方法,本文得到了一类具有反馈控制的概周期时滞差分竞争系统正概周期解的存在性和全局吸引性的充分条件.一个具体的例子说明了主要结论的合理性.     

具有连续变量的多时滞二阶非线性中立型差分方程的振动性

用分析的方法研究了一类具有连续变量的多时滞二阶非线性中立型差分方程解的振动性,给出了该类方程解振动和差分算子振动的几个充分条件.     

带有分段常数变量的单种群模型的全局稳定性和振动性（英文）

研究了带有分段常数变量的单种群连续模型的全局稳定性和振动性.通过计算将连续模型转化为对应的差分模型,首先研究发现当模型的参数和初值条件满足一定条件时,差分方程的任一正解是单调有界的,且正平衡态是全局渐近稳定的.其次以参数β_1作为分类标准,在两种情况下研究得到当参数r属于某一区间时,差分方程的解是振动的.最后数值模拟验证了理论分析的正确性.     

稻纵卷叶螟种群系统动态模拟

本文组建了稻纵卷叶螟种群系统模似模型,它由系统亚模型和总模型二个部分组成.系统亚模型包括发育、死亡和繁殖三个子模块.系统总模型是作者提出的新模型,它综合了前人所提出的种群模型的优点,以差分方程形式给出,以生理时间为单位,考虑了种群内个体间发育速率的差异,不仅能模拟种群数量动态,而且能模拟种群年龄结构,同时能预测发生期.模型有效性检验表明,模拟结果基本上能吻合实测结果.文中还对5个影响因子进行了灵敏性分析.     

稻纵卷叶螟种群系统动态模拟

本文组建了稻纵卷叶螟种群系统模似模型,它由系统亚模型和总模型二个部分组成.系统亚模型包括发育、死亡和繁殖三个子模块.系统总模型是作者提出的新模型,它综合了前人所提出的种群模型的优点,以差分方程形式给出,以生理时间为单位,考虑了种群内个体间发育速率的差异,不仅能模拟种群数量动态,而且能模拟种群年龄结构,同时能预测发生期.模型有效性检验表明,模拟结果基本上能吻合实测结果.文中还对5个影响因子进行了灵敏性分析.     

Red queen dynamics in specific predator–prey systems

The dynamics of a predator–prey system are studied, with a comparison of discrete and continuous strategy spaces. For a \(2 \times 2\) system, the average strategies used in the discrete and continuous case are shown to be the same. It is further shown that the inclusion of constant prey switching in the discrete case can have a stabilising effect and reduce the number of available predator types through extinction.     

Coupled multi-component systems: A simple membrane model

We present initial results regarding the existence, stability and interactionof linear and nonlinear vibrational modes in a system of two coupled, onedimensional lattices with unequal numbers of masses. The effects on thesenonlinear modes of coupling a near continuum system to a discrete systemusing a nonlinear coupling are examined. This numerical model is a firststep towards investigating the dynamical behavior of a flexible sheetcoupled nonlinearly to a semi-rigid support, a system which couldconceivably represent a biological cell membrane with a supporting proteinnetwork. General implications for the dynamical behavior of continuumsystems coupled nonlinearly to discrete systems are introduced.     

Tunable Multi-Fano Resonances in MDM-Based Side-Coupled Resonator System and its Application in Nanosensor

In this paper, two Fano resonances are achieved in the proposed plasmonic system. Theoretical analysis and simulation results show that two discrete states coupled with a continua lead to these Fano resonances. The discrete states are provided by the side-coupled square cavity, and a baffle plate placed in metal-dielectric-metal waveguide is used to produce a continuous transmission spectrum. The resonant wavelengths and the linewidth of these Fano resonances can be easily tuned by adjusting the parameters of system. This system exhibits high sensitivities as high as 850 and 1120 nm/RIU corresponding to two Fano resonances, and the figure of merit can reach to 1.7 × 10⁵ by optimizing the system. By introducing another square cavity, four Fano resonances are obtained which originate from four discrete states coupled with continua, and they can be tuned independently. The flexible multi-Fano resonances system has significant application bio-nanosensor, nonlinear, and slow light devices.     

基于反馈控制离散Lotka-Volterra竞争模型的持续生存和稳定性

针对一类具有偏离自变量的离散Lotka-Volterra竞争模型,考虑到不可避免的外界扰动,通过引入反馈控制,基于一定的分析技巧得到该系统持久性与全局稳定性的充分条件.生态意义上表明:在外界扰动下,具有偏离自变量的离散Lotka-Volterra竞争模型仍能持续生存并保持全局稳定发展.     

Discrete colour polymorphism in the tawny dragon lizard (Ctenophorus decresii) and differences in signal conspicuousness among morphs

Intraspecific colour variation is common in nature and can vary from the coexistence of discrete colour variants in polymorphic species to continuous variation. Whether coloration is continuous or discrete is often ambiguous and many species exhibit a combination of the two. The nature of the variation (discrete or continuous) has implications for both the genetic basis of the colour variation and the evolutionary processes generating and maintaining it. Consequently, it is important to qualify the existence of discrete morphs, particularly in relation to the animal's visual system. In this study, we quantified male throat colour variation in Ctenophorus decresii tawny dragon lizard and tested for morphological and ecological correlates of the colour variants. We confirmed that discrete throat colour morphs can be defined based on colour and pattern analyses independent of the human visual system. We also found that the colour variants differed in their conspicuousness from the background, to the lizard's visual system, which has implications for signalling. However, the morphs did not differ in morphology or microhabitat use, which suggests that these characteristics are not involved in the evolutionary maintenance of the polymorphism.     

Discrete event, multi-level simulation of metabolite channeling

Typically differential equations are employed to simulate cellular dynamics. To develop a valid continuous model based on differential equations requires accurate parameter estimations; an accuracy which is often difficult to achieve, due to the lack of data. In addition, processes in metabolic pathways, e.g. metabolite channeling, seem to be of a rather qualitative and discrete nature. With respect to the available data and to the perception of the underlying system, a discrete rather than a continuous approach to modeling and simulation seems more adequate. A discrete approach does not necessarily imply a more abstract view on the system. If we move from macro to micro and multi-level modeling, aspects of subsystems and their interactions, which have been only implicitly represented, become an explicit part of the model. To start exploring discrete event phenomena within metabolite channeling we choose the tryptophan synthase. Based on a continuous macro model, a discrete event, multi-level model is developed which allows us to analyze the interrelation between structural and functional characteristics of the enzymes.     

A systems-theory approach to the analysis of multiexponential fluorescence decay.

A mathematical model of the fluorescence decay experiment based on linear systems theory is presented. The model suggests an experimental technique that increases the probability of correctly determining the decay constants of a multicomponent system. The use of moment methods for data analysis improves accuracy by combining information obtained from several discrete experiments. Examples are presented to show that the analysis of a three component system composed of known standards is improved as the number of experimental determinations is increased from one to four. The discrete measurements are made by changing the excitation and emission wavelengths.     

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system.     

A coupled discrete/continuum model for describing cancer-therapeutic transport in the lung

We propose a computational simulation framework for describing cancer-therapeutic transport in the lung. A discrete vascular graph model (VGM) is coupled to a double-continuum model (DCM) to determine the amount of administered therapeutic agent that will reach the cancer cells. An alveolar cell carcinoma is considered. The processes in the bigger blood vessels (arteries, arterioles, venules and veins) are described by the VGM. The processes in the alveolar capillaries and the surrounding tissue are represented by a continuum approach for porous media. The system of equations of the coupled discrete/continuum model contains terms that account for degradation processes of the therapeutic agent, the reduction of the number of drug molecules by the lymphatic system and the interaction of the drug with the tissue cells. The functionality of the coupled discrete/continuum model is demonstrated in example simulations using simplified pulmonary vascular networks, which are designed to show-off the capabilities of the model rather than being physiologically accurate.