食饵具有周期强迫的捕食模型

建立并研究了一类具有周期强迫和脉冲扰动的捕食模型,通过理论分析和数值模拟,得到了食饵灭绝周期解全局渐近稳定和系统持久的充分条件,利用分支理论证明了边界周期解附近会分支出正周期解.     

Periodic solution of a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control

In this paper, a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.     

在脉冲污染环境中具有阶段结构的捕食食饵Gompertz模型的动力学性质

研究了在脉冲污染环境中,捕食者具有阶段结构的捕食食饵Gompertz模型的动力学性质,获得了捕食者灭绝周期解全局吸引和系统持续生存的条件.     

一类带Monod增长率及脉冲状态反馈控制的微生物杀虫剂模型的周期解

研究了一类带Monod增长率及脉冲状态反馈控制的微生物杀虫剂模型．证明了无脉冲系统的负向全局渐近稳定性及带有脉冲状态反馈控制系统具有阶一周期解,并且给出阶一周期解存在和稳定的充分条件．数值模拟验证了理论结果．     

Positive effects of proline addition on the central metabolism of wild-type and lactic acid-producing <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> strains

In Saccharomyces cerevisiae, proline is a stress protectant interacting with other substrate uptake systems against oxidative stress under low pH conditions. In this study, we performed metabolomics analysis to investigate the response associated with an increase in cell growth rates and maximum densities when cells were treated with proline under normal and acid stress conditions. Metabolome data show that concentrations of components of central metabolism are increased in proline-treated S. cerevisiae. No consumption of proline was observed, suggesting that proline does not act as a nutrient but regulates metabolic state and growth of cells. Treatment of lactic acid-producing yeast with proline during lactic acid bio-production improved growth rate and increased the final concentration of lactic acid.     

Periodic Solutions of N-Species Competition System with Time Delays

1IntroductionWeconsiderherethefollowingpeiodicn-speCiescompetitionSyStemwithtimedelaystogetherwithinitialvalueconditionswherer,(i=1,..',n)arepeitivecontinuousdeperiedicfUnctionsandail,ry(i,j=1,...f,n)arenormeqativeconStants.Whenr.(i=1,..',n)arepeitiveconStants,(1.1)isknoWnasan"speCies~a-VolterracompetitionsystemintheliteratureonmathematicaleCOIOgyandhashostudiedextensivelybySevelal.thorstl-j.ShibataandAntot')haveshownthetimedelaysinatwcrspeCies~a-Volterra~itionsystemcanleadto"~ic~ior".O…     

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。     

Lipase-catalyzed transformations for the synthesis of butyl lactate: a comparison between esterification and transesterification

The alpha-hydroxy esters are increasingly employed in cosmetic, food, and pharmaceutical formulations as they determine reduced skin-irritant effects in comparison with the respective acids, offering similar hygroscopic, emulsifying, and exfoliating properties. The enzymatic synthesis of lactate esters in nonaqueous systems was studied as regards the influence of the critical process parameters, to enable a comparison between the most commonly used synthetic routes, namely, esterification and transesterification. The experimental results showed that the direct esterification of lactic acid with butanol may be limited by the reduced lipase stability in the presence of the acid (substrate) and of the water (product), in particular when solvent-free media are used. The stability of the enzyme is further reduced as polar solvents are required as a result of the polarity of the lactic acid. Therefore, the use of the lactic acid as substrate is of practical interest only when the acid is significantly cheaper in comparison with its short-chain esters. If this is not the case, the transesterification of the ethyl lactate with butanol is to be preferred for the higher flexibility in the choice of the experimental conditions, the operability of solvent-free systems, and the simplicity of the product removal assembly.     

基于比率的具有反馈控制的非自治捕食系统的动力学行为

讨论了一类基于比率的具有反馈控制的非自治捕食系统,所有的参数都是时滞的.先研究了该系统的一致持久性和全局渐近稳定性,并通过构造适当的Lyapunov函数,得到了系统存在惟一渐近稳定的正概周期解的充分性条件.最后,通过一个例子说明了结论的可行性.     

关于一类非自治阶段结构捕食系统的持久性与周期解

本文研究了一类非自治阶段结构捕食系统的渐近性质,得到在适当的条件下系统的持久性,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。     

具有阶段结构和Leslie-Gower HollingⅡ功能性反应的脉冲食饵-捕食系统(英文)

我们考虑了一个具有阶段结构和Leslie-Gower HollingⅡ功能性反应的时滞脉冲食饵-捕食系统.运用脉冲微分方程的比较定理和小扰动的方法,我们得到了保证系统食饵灭绝周期解的全局渐近稳定性和系统永久持续生存的条件.     

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

In this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Lactic acid production from enzyme-thinned corn starch usingLactobacillus amylovorus

Summary An alternative process for industrial lactic acid production was deveooped using a starch degrading lactic acid producing organism,Lactobacillus amylovorus B-4542. In this process, saccharification takes place during the fermentation, eliminating the need for complete hydrolysis of the starch to glucose prior to fermentation. The cost savings of this alternative are substantial since it eliminates the energy input, separate reactor tank, time, and enzyme associated with the typical pre-fermentation saccharification step. The only pre-treatment was gelatinization and enzyme-thinning of the starch to overcome viscosity problems associated with high starch concentrations and to make the starch more rapidly degradable. This fermentation process was optimized for temperature, substrate level, nitrogen source and level, mineral level, B-vitamins, volatile fatty acids, pH, and buffer source. The rate of the reaction and the final level of lactic acid obtained in the optimized liquefied starch process was similar to that obtained withL. delbrueckii B-445 using glucose as the substrate.     

The dynamics of a Lotka–Volterra predator–prey model with state dependent impulsive harvest for predator

According to the economic and biological aspects of renewable resources management, we propose a Lotka–Volterra predator–prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex.     

降解尿酸乳酸菌复合菌系的筛选与菌株组合提升降解效果

【背景】高尿酸症由血液中尿酸含量明显升高而导致,利用乳酸菌对人体的益生作用缓解高尿酸血症越来越受到关注。【目的】获得具有降解尿酸能力的乳酸菌复合菌系与纯培养菌株。【方法】以泡菜为样品来源,以尿酸为底物,采用MRS培养基筛选降解尿酸的乳酸菌复合菌系,通过高效液相色谱法测定复合菌系对尿酸的降解能力。【结果】得到一组乳酸菌复合菌系,当培养温度为37 °C、pH值为6.20、静置培养72 h后复合菌系对尿酸的降解率为12.08%;通过优化培养条件,当该菌系在以牛肉膏为单一氮源、初始pH值为5.00、温度为35 °C的条件下培养72 h,尿酸降解率上升至17.19%,降解率比优化前提高了42.3%;从该菌系中分离出两株具有尿酸降解能力的菌株UA-1与UA-2,它们的尿酸降解率分别为10.85%和8.65%;通过形态学观察和16S rRNA基因序列分析,经鉴定两株菌均为布氏乳杆菌(Lactobacillus buchneri)。将两株单菌组合降解尿酸试验发现,UA-1与UA-2比例为2:1的尿酸降解率为20.2%,比原复合菌系的降解能力提高了67.22%。【结论】研究证明了乳酸菌复合菌系对尿酸的降解能力优于单个菌株,为后续利用乳酸菌复合菌系应用提供了数据支持。     

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.     

多种群阶段结构竞争系统的周期解与概周期解

研究具有阶段结构的多种群竞争系统,得到该系统一致持久,正周期解全局渐近稳定及概周期解的存在性与一致渐近稳定性的充分条件。     

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.     

Dynamics of a biochemical system with multiple oscillatory domains as a clue for multiple modes of neuronal oscillations

We analyze the behavior of a two-variable biochemical model in conditions where it admits multiple oscillatory domains in parameter space. The model represents an autocatalytic enzyme reaction with input of substrate both from a constant source and from non-linear recycling of product into substrate. This system was previously studied for birhythmicity, i.e. the coexistence between two stable periodic regimes (Moran and Goldbeter 1984), and for multithreshold excitability (Moran and Goldbeter 1985). When two distinct oscillatory domains obtain as a function of the substrate injection rate, the system is capable of exhibiting two markedly different modes of oscillations for slightly different values of this control parameter. Phase plane analysis shows how the multiplicity of oscillatory domains depends on the parameters that govern the underlying biochemical mechanism of product recycling. We analyze the response of the model to various kinds of transient perturbations and to periodic changes in the substrate input that bring the system through the two ranges of oscillatory behavior. The results provide a qualitative explanation for experimental observations (Jahnsen and Llinas 1984b) related to the occurrence of two different modes of oscillations in thalamic neurones.