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.     

具脉冲收获与脉冲单边扩散的单种群动力学模型研究

建立了一类具脉冲收获与脉冲单边扩散在不同固定脉冲时刻的单种群动力学模型利用离散动力系统频闪映射理论,得到了脉冲收获的阈值.该结论说明只要收获量不超过其阈值通过扩散则种群可以保持持续生存.     

具有质体的非均匀恒化器模型正解的长时行为

本文讨论了一类具有质体非均匀恒化器模型解的持续性,首先利用上下解方法与极值原理得到恒化器模型的先验估计;然后利用非线性系统的持续性理论讨论恒化器模型正解的长时行为,并且得到了当模型中的参数满足特定条件时,该模型对应的半动力系统是强一致连续持续的.     

具脉冲出生与脉冲收获切换的阶段结构单种群动力学模型

本文建立具脉冲出生与脉冲收获切换的阶段结构单种群动力学模型.利用离散动力系统的相关理论,得到生物生存与灭绝的相关控制阈值,并提出相关的生物保护性理论建议.     

分数阶SIR传染病模型的稳定性分析（英文）

本文研究一类Caputo型分数阶SIR传染病模型的全局稳定性.首先,通过对方程进行求解得到了模型的平衡点.然后,根据关于Caputo型分数阶微积分的一个引理和分数阶动力系统的相关理论,分别构造相应的Lyapunov函数判断平衡点的稳定性.结果表明,当R_01时,模型有唯一的无病平衡点E_0,E_0是全局稳定的;如果R_01时,模型存在无病平衡点E_0和地方病平衡点E_*,E_*是全局稳定的.最后,给出了一些数值模拟来验证理论分析的结果.     

具两系统切换脉冲单种群动力学模型

建立具两系统切换脉冲单种群动力学模型,利用离散动力系统频闪映射理论,得到系统种群灭绝与系统种群持续生存的控制阈值.结果表明脉冲收获与冬眠期对于系统种群持久起着重要作用,从而为现实的生物资源管理与生物多样性保护提供了可靠的策略依据.     

一类具年龄结构的线性周期种群动力系统的最优控制

研究一类具有年龄结构的线性周期种群线性动力系统的最优控制问题,即讨论了具有周期的生死率和周期变化的控制项的模型．利用Mazur's定理,证明了最优控制问题最优解的存在性,同时由法锥概念的特征刻画,我们还得到了最优控制问题最优解存在的必要条件．     

一类Kolmogorov系统全局稳定性分析

以K单调动力系统理论为基础,通过构造伴随系统,给出了保证一类Kolmogrov系统正平衡点全局稳定性的充分条件,并用此结论验证了Lotka-Volterra系统和二维的Kolomgorv食饵-捕食系统的全局稳定性,改进了Simth关于K单调理论的结果.     

具脉冲出生和脉冲收获的基因突变单种群动力学模型分析

建立了具脉冲出生和脉冲收获的基因突变单种群动力学模型.利用离散动力系统的频闪映射理论,得到了生物资源管理控制阈值的充分条件.     

具脉冲收获切换单种群动力学模型控制阈值研究

建立具脉冲收获切换单种群动力学模型,利用离散动力系统频闪映射理论,得到系统种群灭绝与系统种群持续生存的控制阈值.结果表明一个周期内适当的二次收获种群对系统种群持久起着重要作用,从而为现实的生物资源管理与生物多样性保护提供了可靠的策略依据.     

Dynamical entropy via entropy of non-random matrices: Application to stability and complexity in modelling ecosystems

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems.     

Development of semi-continuous and continuous flow bioreactors for the high level production of chloroperoxidase

Summary Continuous and semi-continuous flow bioreactors have been developed for the production of chloroperoxidase, which is secreted by the fungusCaldariomyces fumago. The semi-continuous system facilitated the harvest of mycelium-free supernatant for 200 days from a single inoculum, with enzyme levels greater than 600 mg/l during the first 80 days. The continuous flow bioreactor yielded essentially pure enzyme at the rate of 117 mg/day.     

具脉冲扩散效应的单种群动力学模型

讨论了两斑块间脉冲扩散的单种群动力学模型,利用离散动力系统频闪映射理论,得到了种群持续生存的充分条件．结论31,1~了现实的生物种群动力学性质,也丰富了脉冲微分方程理论．     

Fundamental analysis of real-time PCR quantification and modeling for thermophilic <Emphasis Type="SmallCaps">L</Emphasis>-lactate fermentation by <Emphasis Type="Italic">Bacillus coagulans</Emphasis> from glucose

Batch and semi-continuous thermophilic l-lactate fermentation experiments were performed using Bacillus coagulans and glucose as a substrate. Reactor performance and biomass concentrations were assessed using two methods: turbidity as a traditional biomass index and real-time polymerase chain reaction (PCR) quantification of 16S rRNA genes. In the batch experiment, although the relationship between turbidity and real-time PCR assay differed depending on the growth phase, a correlation was observed between both assay methods. In the semi-continuous experiment, real-time PCR measurement was well suited for use as an index for evaluating bacterial mass under different organic loading conditions. A mathematical model was applied to evaluate the real-time PCR quantification to long-term, semi-continuous lactate fermentation. Lactate fermentation was well suited since only B. coagulans was involved in the reactions. The results obtained revealed a fundamental relationship between real-time PCR and traditional biomass analyses.     

Batch and semi-continuous microalgal TAG production in lab-scale and outdoor photobioreactors

Microalgal triglycerides (TAGs) represent a sustainable feedstock for food, chemical and biofuel industries. The operational strategy (batch, semi-continuous, continuous cultivations) has an impact on the TAG productivity. In this study, semi-continuous (i.e. with fixed harvesting frequency) and batch cultivations were compared on TAG production both at lab-scale and in outdoor cultivations. At lab-scale, the semi-continuous TAG productivity was highest for a cycle time of 2 days (SC1; 0.21 g L^?1 day^?1) and similar to the maximum obtained with the batch (optimal harvest time; 0.23 g L^?1 day^?1). Although TAG content was lower for SC1 (22 %) than for the batch (35 %), higher biomass productivities were obtained with SC1. Outdoors, semi-continuous cultivations were subjected to a lower degree of stress (i.e. higher amount of nitrogen present in the system relative to the given irradiance) compared to lab-scale. This yielded low and similar TAG contents (10–13 %) in the different semi-continuous runs that were outdone by the batch on both TAG content (15–25 %) and productivity (batch, 0.97–2.46 g m^?2 day^?1; semi-continuous, 0.35–0.85 g m^?2 day^?1). The lab-scale experiments showed that semi-continuous strategies, besides leading to similar TAG productivities compared to the batch, could make TAG production cost effective by valorising also non-TAG compounds. However, optimization of outdoor semi-continuous cultivations is still required. For instance, the nitrogen supply and the harvest frequency should be adjusted on the total irradiance. Additionally, future research should focus on recovery metabolism upon nitrogen resupply.     

Understanding original antigenic sin in influenza with a dynamical system

Original antigenic sin is the phenomenon in which prior exposure to an antigen leads to a subsequent suboptimal immune response to a related antigen. Immune memory normally allows for an improved and rapid response to antigens previously seen and is the mechanism by which vaccination works. I here develop a dynamical system model of the mechanism of original antigenic sin in influenza, clarifying and explaining the detailed spin-glass treatment of original antigenic sin. The dynamical system describes the viral load, the quantities of healthy and infected epithelial cells, the concentrations of naïve and memory antibodies, and the affinities of naïve and memory antibodies. I give explicit correspondences between the microscopic variables of the spin-glass model and those of the present dynamical system model. The dynamical system model reproduces the phenomenon of original antigenic sin and describes how a competition between different types of B cells compromises the overall effect of immune response. I illustrate the competition between the naïve and the memory antibodies as a function of the antigenic distance between the initial and subsequent antigens. The suboptimal immune response caused by original antigenic sin is observed when the host is exposed to an antigen which has intermediate antigenic distance to a second antigen previously recognized by the host''s immune system.     

On the Stock Estimation for a Harvested Fish Population

We consider a stage-structured model of a harvested fish population and we are interested in the problem of estimating the unknown stock state for each class. The model used in this work to describe the dynamical evolution of the population is a discrete time system including a nonlinear recruitment relationship. To estimate the stock state, we build an observer for the considered fish model. This observer is an auxiliary dynamical system that uses the catch data over each time interval and gives a dynamical estimate of the stock state for each stage class. The observer works well even if the recruitment function in the considered model is not well known. The same problem for an age-structured model has been addressed in a previous work (Ngom et al., Math. Biosci. Eng. 5(2):337–354, 2008).     

Semi-continuous operation of the insect cell — Baculovirus system

Summary The insect cell - baculovirus system is used to synthesize a variety of recombinant proteins, generally in a batch system. We have developed a semi-continuous system and studied its operation at three different residence times. The resulting data showed that beta-galactosidase can be produced for 50 to 150 hours longer than the batch system.