一类具有时滞的传染病模型的稳定性分析

研究了一类具有时滞的传染病生物模型．首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式．     

一具有非线性发生率传染病模型的稳定性和霍普夫分支

在这篇文章中,我们研究了一具有非线性发生率的传染病模型．该模型经历了鞍结点分支和霍普夫分支．我们对模型的霍普夫分支进行了详细的分析,得知该霍普夫分支是超临界的．此外,我们给出了支持理论分析的数值模拟．     

三种竞争种群的古典Gause-Lotka-Volterra系统

本文讨论了三种竞争种群的古典GLV系统．对系统所有非负平衡点的稳定性,进行了分析,给出了正平衡点全局稳定的充分条件,应用Hopf分支定理,我们给出了系统具有分支值的充分条件．     

具脉冲出生的Leslie-Gower捕食者-食饵系统的动力学分析

研究了一个具有脉冲出生的Leslie-Gower捕食者一食饵系统的动力学性质．利用频闪映射。得到了带有Ricker和Beverton-Holt函数的脉冲系统准确的周期解．通过Floquet定理和脉冲比较定理,讨论了该系统的灭绝和持久生存．最后,数值分析了以b（p）为分支参数的分支图,得到的结论是脉冲出生会带给系统倍周期分支、混沌以及在混沌带中出现周期窗口等复杂的动力学行为．     

双密度制约的Holling Ⅱ型捕食动力系统的定性分析

研究食饵具有非线性密度制约捕食者具有线性密度制约的HollingⅡ型捕食动力系统．以食饵的环境容纳量为分支参数,由Hopf分支得到小振幅极限环的存在性,同时也得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件．     

一类Hodgkin-Huxley模型的分支研究

考虑一类描述肌细胞膜电位变化的Hodgkin-Huxley模型的分支问题.利用常微分方程的分支理论,结合数值模拟结果,对模型的单参数分支与双参数分支进行了讨论.分析了Bogdanov-Takens分支,得到了相应的鞍结点分支曲线,Hopf分支曲线与同宿分支曲线.     

一类三阶时滞微分系统的稳定性与Hopf分支研究

给出了一类三阶时滞微分系统的局部稳定性判断．并由规范型理论及中心流型定理推导出诸如方向,稳定性及周期等分支性质．最后由具体例子模拟来验证计算的正确性．     

一类考虑收获的Monod-Haldane型捕食系统的动力学行为(英文)

给出了一类考虑收获的Monod-Haldane型捕食者-食饵系统的平衡点和稳定性分析,及给出几类分支的分析,包括鞍结分支、Bogdanov-Takens分支、超临界和亚临界Hopf分支,最后给出了数值模拟例子验证了结论的正确性.     

一类具连续时滞的捕食-被捕食生态系统

本文讨论了一类具有强连续时滞的捕食-被捕食模型,分析了各非负平衡点的稳定性,利用区域连续收缩方法,得出非负平衡点全局稳定的充分条件,给出正平衡点全局稳定的充分条件,并给出系统出现Hopf的分支值．     

一类信号转导通路模型参数辨识中最小应测量状态的确定

建立信号转导通路的数学模型是系统生物学的一个重要目标．但是信号转导通路本身的复杂结构及其所表现出的强非线性特征,使得对该类模型的参数辨识十分困难．参数辨识所需要的测量数据的选择对于辨识结果有重要影响．本文研究了一类信号转导通路模型参数辨识中最小应测量状态的计算问题．给出了用于确定该最小应测量状态的目标函数,通过对目标函数进行简单的运算,确定了用来估计未知参数的最小应测量状态的数量,同时给出了一种计算系统状态对应于未知参数的敏感性系统曲线的新方法．以TNFα诱导的NF-κB信号转导通路为例进行了仿真研究,并给出了仿真结果．     

非线性红松林生态系统的定性与分支研究(英文)

利用系统分析的方法研究了一类非线性红松林生态系统的稳定性,讨论了其鞍结分支和Hopf分支,且对Hopf分支周期解进行了详细的分析和计算,指出了红松林生态系统中松籽、鼠类和幼苗三种群数量具有周期波动的特征.     

Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

An susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.     

延迟遗传调控网络稳定性及分支

本文主要研究了延迟遗传调控网络的局部稳定性和该网络的Hopf分支存在条件．延迟遗传调控网络是无穷维系统,此类系统在平衡点线性化后的特征方程为超越方程。通过对此超越方程进行研究,得到了系统系数不同时的系统稳定的条件及相关结论,又进一步说明了此系统的Hopf分支存在条件．最后,举一个例子进行了数值仿真验证了所得到的结论．     

Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species

In this paper, a predator–prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.     

一类时滞神经网络模型的稳定性与全局Hopf分支

研究了一类由两个神经元构成的时滞神经网络模型的稳定性和局部Hopf分支,并结合一般泛函微分方程的全局Hopf分支定理,利用度理论研究了全局Hopf分支的存在性．     

Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays

Time delay is an inevitable factor in neural networks due to the finite propagation velocity and switching speed. Neural system may lose its stability even for very small delay. In this paper, a two-neural network system with the different types of delays involved in self- and neighbor- connection has been investigated. The local asymptotic stability of the equilibrium point is studied by analyzing the corresponding characteristic equation. It is found that the multiple delays can lead the system dynamic behavior to exhibit stability switches. The delay-dependent stability regions are illustrated in the delay-parameter plane, followed which the double Hopf bifurcation points can be obtained from the intersection points of the first and second Hopf bifurcation, i.e., the corresponding characteristic equation has two pairs of imaginary eigenvalues. Taking the delays as the bifurcation parameters, the classification and bifurcation sets are obtained in terms of the central manifold reduction and normal form method. The dynamical behavior of system may exhibit the quasi-periodic solutions due to the Neimark- Sacker bifurcation. Finally, numerical simulations are made to verify the theoretical results.     

Analysis of bifurcations in continuous fermentation using recombinant microorganisms with delayed responses

When the feed rate to a fermenter is varied periodically in order to favor the growth of plasmid-containing cells, a transition may occur from the starting stationary state to another state. The resulting state may be constant or oscillatory. A generalised model based on the adaption times of plasmid-free and plasmid-harboring cells has been used. Analytical conditions have been derived for bifurcation from one nonoscillatory state to another or to an oscillatory state (Hopf bifurcation). The frequency of oscillation is shown to have an upper bound, which can be controlled by manipulating certain process parameters. The production of tryptophan synthetase by the plasmid pPLc23trpAl in E. coli is used as an example to determine the nature of the Hopf bifurcations.     

Material recycling in a closed aquatic ecosystem. I. Nitrogen transformation cycle and preferential utilization of ammonium to nitrate by phytoplankton as an optimal control problem

A mathematical model of the nitrogen transformation cycle in an aquatic environment is studied. Using Pontryagin's maximum principle, a preferential utilization of ammonium to nitrate by phytoplankton is explained and verified by experimental data. A multiparameter bifurcation is given. The model was found to have four types of equilibrium sets. It is shown that a Hopf bifurcation may occur.