双营养Chemostat模型周期解的全局吸引性

研究含有时滞的双营养单种群Ｃｈｅｍｏｓｔａｔ模型周期解的全局吸引性,首先利用强正、凹算子理论给出了系统存在唯一正周期解的充分条件,然后利用泛函微分方程的单调理论得到了正周期解的全局吸引性。     

Global dynamics of a chemostat competition model with distributed delay

 We study the global dynamics of n-species competition in a chemostat with distributed delay describing the time-lag involved in the conversion of nutrient to viable biomass. The delay phenomenon is modelled by the gamma distribution. The linear chain trick and a fluctuation lemma are applied to obtain the global limiting behavior of the model. When each population can survive if it is cultured alone, we prove that at most one competitor survives. The winner is the population that has the smallest delayed break-even concentration, provided that the orders of the delay kernels are large and the mean delays modified to include the washout rate (which we call the virtual mean delays) are bounded and close to each other, or the delay kernels modified to include the washout factor (which we call the virtual delay kernels) are close in L ¹-norm. Also, when the virtual mean delays are relatively small, it is shown that the predictions of the distributed delay model are identical with the predictions of the corresponding ODEs model without delay. However, since the delayed break-even concentrations are functions of the parameters appearing in the delay kernels, if the delays are sufficiently large, the prediction of which competitor survives, given by the ODEs model, can differ from that given by the delay model. Received: 9 August 1997 / Revised version: 2 July 1998     

Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor

The asymptotic behavior of solutions of a model for competition between plasmid-bearing and plasmid-free organisms in the chemostat with two distributed delays and an external inhibitor is considered. The model presents a refinement of the one considered by Lu and Hadeler [Z. Lu, K.P. Hadeler, Model of plasmid-bearing plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Math. Biosci. 167 (2000) p. 177]. The delays model the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition. Furthermore, it is assumed that there is inter-specific competition between the plasmid-bearing and plasmid-free organisms as well as intra-specific competition within each population. Conditions for boundedness of solutions and existence of non-negative equilibrium are given. Analysis of the extinction of the organisms, including plasmid-bearing and plasmid-free organisms, and the uniform persistence of the system are also carried out. By constructing appropriate Liapunov-like functionals, some sufficient conditions of global attractivity to the extinction equilibria are obtained and the combined effects of the delays and the inhibitor are studied.     

Effects of sea surface warming on marine plankton

Ocean warming has been implicated in the observed decline of oceanic phytoplankton biomass. Some studies suggest a physical pathway of warming via stratification and nutrient flux, and others a biological effect on plankton metabolic rates; yet the relative strength and possible interaction of these mechanisms remains unknown. Here, we implement projections from a global circulation model in a mesocosm experiment to examine both mechanisms in a multi‐trophic plankton community. Warming treatments had positive direct effects on phytoplankton biomass, but these were overcompensated by the negative effects of decreased nutrient flux. Zooplankton switched from phytoplankton to grazing on ciliates. These results contrast with previous experiments under nutrient‐replete conditions, where warming indirectly reduced phytoplankton biomass via increased zooplankton grazing. We conclude that the effect of ocean warming on marine plankton depends on the nutrient regime, and provide a mechanistic basis for understanding global change in marine ecosystems.     

具有时滞和反馈控制的Logistic增长模型的正周期解

首次研究同时具有状态依赖时滞和连续时滞的反馈控制Logistic增长模型,利用重合度理论研究其正周期解的存在性问题,得到了该系统周期正解存在的充分性条件,同时通过构造适当地Lyapunov泛函得到保证该系统（在适当限制下）存在全局稳定周期解的充分性条件,得到一些新结果,所得结果推广和改进了相关文献的主要结果。     

具有可变时滞的非自治离散Logistic方程的全局吸引性

得到了具有可变时滞的非自治离散Logistic方程的正解收敛于方程的正平衡常数的一系列充分条件和振动准则．     

具有时滞的非自治差分竞争系统的渐近行为研究(英文)

提出了一个具有时滞的非自治差分竞争系统.分别利用差分不等式及Lyapunov离散函数技巧,得到了系统永久持续生存和正解全局吸引的充分条件.数值模拟验证了理论结果的正确性.     

具收获与脉冲的时滞捕食模型研究

研究了与生物资源管理相关的食饵具脉冲扰动与成年捕食者具连续收获的阶段结构时滞捕食-食饵模型.利用离散动力系统的频闪映射和脉冲时滞微分方程理论,得到了捕食者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.结论为现实的可再生生物资源管理提供了可靠的策略依据.     

Permanence and global attractivity for Lotka–Volterra difference systems

 The permanence and global attractivity for two-species difference systems of Lotka–Volterra type are considered. It is proved that a cooperative system cannot be permanent. For a permanent competitive system, the explicit expression of the permanent set E is obtained and sufficient conditions are given to guarantee the global attractivity of the positive equilibrium of the system. Received: 21 May 1997 / Revised version: 25 November 1998     

Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate

In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov functionals and using the Lyapunov–LaSalle invariance principle, we prove the global stability of the endemic equilibrium and the disease-free equilibrium for time delays of any length in each model. Our results show that the global properties of equilibria also only depend on the basic reproductive number and that the latent period in a vector does not affect the stability, but the latent period in an infected host plays a positive role to control disease development.     

Contrasting effects of a cladoceran (Daphnia galeata) and a calanoid copepod (Eodiaptomus japonicus) on algal and microbial plankton in a Japanese lake, Lake Biwa

Macrozooplankton may affect algal and microbial plankton directly through grazing or predation and indirectly through nutrient regeneration. They may also affect potential prey positively by removing alternative predators. Here, we examined the effects of a cladoceran (Daphnia) and a calanoid copepod (Eodiaptomus) on algal and microbial plankton in a Japanese lake using in situ experiments in which we manipulated the nutrient supply and biomass of these macrozooplankton. The response of algal and microbial plankton to macrozooplankton was diverse and varied depending on the level of nutrient supply. Eodiaptomus seemed to feed mainly on large algae (>20 µm) and microzooplankton, while direct grazing by Daphnia on algae, bacteria, heterotrophic nanoflagellates (HNF), and microzooplankton (ciliates, heliozoa, and rotifers) was pronounced. Trophic linkages within these microbial plankton was also suggested; bacteria were grazed by HNF and these in turn were grazed by microzooplankton. When the nutrient supply was high, both HNF and microzooplankton were exposed to higher amounts of algae and lower bacterial abundance. Moreover, nutrient regeneration by daphnids and Eodiaptomus copepods seemed to differentially stimulate the growth of algae and bacteria. The results suggest that the relationship between macrozooplankton and microbial plankton cannot be fully understood without taking into consideration not only the feeding characteristics of the macrozooplankton, but also the food web structure, the subsidized algal resource, and nutrient regeneration from the macrozooplankton.     

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.     

一个造血模型的全局吸引性和周期解相交

本文将Mackey和Glass提出的一个造血模型推广到具有周期系数和无穷时滞的情形．研究该模型的全局吸引性和周期解相交,并相应地得到两个充分条件.     

Asymptotic behaviour of positive solutions of periodic delay logistic equations

The delay logistic equation with periodic coefficients is studied. Under condition (2.1) below the existence and global attractivity of a unique periodic solution is proved by mean of monotonicity methods.Work partially supported by G.N.A.F.A.-C.N.R.     

Shifting Regimes and Changing Interactions in the Lake Washington,U.S.A., Plankton Community from 1962–1994

Understanding how changing climate, nutrient regimes, and invasive species shift food web structure is critically important in ecology. Most analytical approaches, however, assume static species interactions and environmental effects across time. Therefore, we applied multivariate autoregressive (MAR) models in a moving window context to test for shifting plankton community interactions and effects of environmental variables on plankton abundance in Lake Washington, U.S.A. from 1962–1994, following reduced nutrient loading in the 1960s and the rise of Daphnia in the 1970s. The moving-window MAR (mwMAR) approach showed shifts in the strengths of interactions between Daphnia, a dominant grazer, and other plankton taxa between a high nutrient, Oscillatoria-dominated regime and a low nutrient, Daphnia-dominated regime. The approach also highlighted the inhibiting influence of the cyanobacterium Oscillatoria on other plankton taxa in the community. Overall community stability was lowest during the period of elevated nutrient loading and Oscillatoria dominance. Despite recent warming of the lake, we found no evidence that anomalous temperatures impacted plankton abundance. Our results suggest mwMAR modeling is a useful approach that can be applied across diverse ecosystems, when questions involve shifting relationships within food webs, and among species and abiotic drivers.     

变系数变时滞BAM神经网络概周期解的存在性与全局吸引性

利用指数二分性、Banach不动点定理与微分不等式分析技巧,在不要求激活函数有界的条件下,给出了变系数变时滞的BAM神经网络概周期解的存在唯一性和全局吸引性的充分条件．所得结果推广和改进了相应文献的结果。对设计BAM神经网络概周期振荡有重要意义．     

Tissue Damage Disrupts Developmental Progression and Ecdysteroid Biosynthesis in Drosophila

In humans, chronic inflammation, severe injury, infection and disease can result in changes in steroid hormone titers and delayed onset of puberty; however the pathway by which this occurs remains largely unknown. Similarly, in insects injury to specific tissues can result in a global developmental delay (e.g. prolonged larval/pupal stages) often associated with decreased levels of ecdysone – a steroid hormone that regulates developmental transitions in insects. We use Drosophila melanogaster as a model to examine the pathway by which tissue injury disrupts developmental progression. Imaginal disc damage inflicted early in larval development triggers developmental delays while the effects are minimized in older larvae. We find that the switch in injury response (e.g. delay/no delay) is coincident with the mid-3rd instar transition – a developmental time-point that is characterized by widespread changes in gene expression and marks the initial steps of metamorphosis. Finally, we show that developmental delays induced by tissue damage are associated with decreased expression of genes involved in ecdysteroid synthesis and signaling.     

Effects of increasing nutrient supply and omnivorous feeding on the size spectrum slope: a size-based nutrient-phytoplankton-zooplankton model

Size spectrum slope has been considered as an indicator for system productivity and size-dependent trophic interactions in plankton communities. We investigated the effect of new nutrient flux (N _in ) and feeding breadth of zooplankton (σ²) on spectral slopes of the plankton community using a size-structured nutrient-phytoplankton-zooplankton model. We studied two types of plankton systems (1) at a steady state and (2) with fluctuating plankton populations. For the steady state systems, the spectral slopes increased with N _in and σ². In contrast, for the systems in fluctuation, spectral slopes constructed from long-term average plankton populations decreased with increasing N _in and σ². In addition to spectral slopes constructed from long-term average population densities, we investigated slope variability in systems with fluctuating plankton populations. The variability of spectral slopes was found to increase with N _in and σ², indicating that spectral slope variation is large in a eutrophic system or when zooplankton feed on a wide size range of prey. Empirically, because N _in is difficult to measure, nutrient concentration is investigated instead. Our model predicts that the spectral slope is positively correlated with nutrient concentration due to the accumulated mesozooplankton biomass, which was confirmed by our study in plankton community in a subtropical reservoir in Taiwan.     

Plankton blooms induced by turbulent flows

Plankton play an important role in the ecology of the ocean and the climate because of their participation in the global carbon cycle at the base of the food chain. However, damaging plankton blooms can sometimes occur and are initially characterized by sudden transient increases in the phytoplankton population. They are thought to be driven by several effects, such as seasonal variations in temperature and salinity, and nutrient mixing. Furthermore, phytoplankton and zooplankton have different buoyancy properties, leading to a differential response in turbulent environments. In this paper, we investigate this effect in a model of advected plankton dynamics. We find that, over a range of parameter values, flows of marine species subjected to inertial/viscous forces naturally lead to patchiness and, in turn, periodically sustained plankton blooms.     

The influence of viral infection on a plankton ecosystem undergoing nutrient enrichment

It is increasingly recognised that viruses are a significant active component of oceanic plankton ecosystems. They play an important role in biogeochemical cycles as well as being implicated in observed patterns of species abundance and diversity. The influence of viral infection in plankton ecosystems is not fully understood. Here we use a number of well-founded mathematical models to investigate the interplay of the ecological and epidemiological interactions of plankton and viruses in the sea. Of particular interest is the role of nutrient on the population dynamics. Nutrient forcing has been suggested as a means of absorbing excess anthropogenic atmospheric carbon dioxide by stimulating increased phytoplankton primary productivity. Here we show that enriching nutrient levels in the sea may decrease the amount of infected phytoplankton species thereby additionally enhancing the efficiency of the biological pump, a means by which carbon is transferred from the atmosphere to the deep ocean.