共查询到10条相似文献，搜索用时 15 毫秒
1.
建立并分析了一类总人口变动的包含具有差异性两子群的单种群的SIRS传染病模型.当基本再生率R_0≤1时,系统仅存在无病平衡点,且它是全局渐近稳定的.当R_0 >1时,存在唯一的地方病平衡点,并且它存在即局部渐近稳定.通过Lyapunov函数法建立了地方病平衡点全局渐近稳定的充分条件.Abstract： An SIRS epidemiological model for a single species population with varying size and two discrepant sub-groups is formulated and analyzed.If the basic reproduction rate R_0≤ 1, only the disease-free equilibrium exists, which proves to be globally asymptotically stable.There exists a unique endemic equilibrium if R_0 > 1 and it is local-ly asymptotically stable whenever it exists.Sufficient conditions are obtained for global asymptotic stability of the endemic equilibrium via the method of Lyapunov functions. 相似文献
2.
提出了水生生态系统中有竞争和捕食的一类简单食物网模型.首先讨论了平衡点的存在条件,利用Hurwitz判据分析了局部渐近稳定性;通过构造Lyapunov函数得到了系统全局渐近稳定的条件,并具体解释了其生物含义.从以上讨论中得到了控制3类物种存活、灭绝或共存的4个阈值.生物分析表明,水草和鱼在控制富营养化问题中起着极其重要的作用.Abstract： In this paper, a simple food web model with competition and predation in aquatic ecosystems is proposed.The existence conditions of equilibria are discussed and the local asymptotic stability is analyzed.By means of Lya-punov functions, the global asymptotic stability of the model is obtained.Four thresholds, which indicate the coex-istence, survival or extinction of 3 species, are obtained from the above discussions.Bio-analysis shows that aquatic weeds and fish play an important role in the control of eutrophication. 相似文献
3.
应用微分方程定性理论,研究了一类具有非线性发生率的SIS传染病模型.给出了该系统极限环的存在性、唯一性以及无病平衡点和地方病平衡点的全局渐近稳定性的充分条件.Abstract： An epidemiological model with nonlinear incidence is studied. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence and uniqueness of the limit cycles and the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium to the system. 相似文献
4.
研究一类具有非线性接触率和垂直传染且在急慢性阶段均传染的非线性SACS传染病侍播数学模型动力学性质,确定了各类平衡点存在的条件阈值,讨论了各平衡点的稳定性,并将会在临界值处出现Hopf分支,揭示了急慢性阶段传染对疾病发展趋势的共同影响.Abstract： The dynamics of a nonlinear SACS epidemic model with vertical transmission, which has infective force at both acute and chronic stages, is studied. The conditions and thresholds for the existence of various equilibria are established. The stability of equilibria is discussed, and periodic solutions may appear by Hopf bifurcation. The influence of infectivity at acute and chronic stages on the developing trend of the disease is disclosed. 相似文献
5.
分析了一个具有季节性种群生长和疾病传播的离散传染病模型.如果基础再生教0< R0 <1,非平凡的无病平衡点是全局稳定的,而当R0>1,模型存在唯一的正平衡点并且在适当的紊件下存在Naimark-Sackep分支.此外,如果分支点处的特征值的辅角是有理敷或无理数,则模型的解是周期的或拟周期的.Abstract： In this paper, we analyze a discrete epidemic model with seasonal population reproduction and disease transmission. If the basic reproduction number 0< R0 < 1, the nontrivial disease-free equilibrium is globally stable; if R0 > 1, there exists a unique positive equilibrium and the model undergoes a Naimark-Saeker bifurcation under suitable conditions; and if the argument of eigenvalue at the bifurcation point is rational or irrational, the solution of the model is periodic or quasiperiodic, respectively. 相似文献
6.
研究了满足齐次Neumann边界条件的一类带有食饵保护的扩散Leslie-Cower型捕食系统.讨论了系统的长时间行为,包括系统的全局吸引子和持久性,并分别运用线性化方法和Lyapunov函数方法得到了系统唯一正常数平衡态的局部稳定性和全局稳定性.Abstract： This paper is concerned with a diffusive Leslie-Gower type predator-prey system tier homogeneous Neu-mann boundary conditions, studies the large time behavior of this system, including the persistence of its global at-tractor, and obtains the local/global asymptotic stability of the unique positive constant steady state of the system with the linearization method and by constructing a suitable Lyapunov function. 相似文献
7.
在假设细胞内免疫反应有时间延迟的情况下对一个病毒感染模型的动力学形态进行了分析.研究了非负平衡点的稳定性和Hopf分支的存在性,并利用规范型和中心流形理论得出了分支方向、周期解的稳定性及周期的公式.Abstract： The dynamics of a viral infection model is analyzed under the assumption that the intracellular immune response is retarded. Stability of nonnegative equilibria and existence of Hopf bifurcation are studied. Using normal form theory and center manifold argument, we calculate the explicit formulas to determine the direction, stability and period of the bifurcating periodic solutions. 相似文献
8.
研究了免疫反应具有两种来源的乙肝病毒模型.通过对相应特征方程的分析,讨论了感染平衡态和未感染平衡态的局部稳定性,证明了基本再生数>1时疾病的持续性.通过几何方法的应用,得到了感染平衡点全局稳定性的充分条件.Abstract： In this paper,an HBV model with activated immune response of two sources is studied.By analyzing the corresponding characteristic equations,the local stability of an infected steady state and an uninfected steady state is discussed.It is proved that if the basic reproductive number is more than one,the disease is persistent.By applying a geometric method,sufficient conditions are obtained for the global stability of the endemic equilibrium. 相似文献
9.
LIUYu ZENGMing SUBao-ku 《勤云标准版测试》2005,(2):144-149
A robust repetitive control scheme is used to improve the rate smoothness of a brushless DC motor (BLDCM) driven test turntable. The method synthesizes variable structure control (VSC) laws and repetitive control (RC) laws in a complementary manner. The VSC strategy can stabilize the system and suppress uncertainties, such as the aperiodic disturbance and noises, while RC strategy can eliminate the periodic rate fluctuation in a steady state. The convergence of the repetitive learning process is also guaranteed by VSC. A general nonlinear system model is discussed. The model can be considered as an extension of BLDCMs. The stability and asymptotic position tracking performance are validated by using Lyapunov functions. Simulation results show the effectiveness of the proposed approach for improving the rate smoothness. 相似文献
10.
针对一类非线性三阶时滞系统构造出了一个合理的Lyapunov函数,去除了要求lyapunov函数趋于无穷大这个较强的条件约束,只要求系统正半轨线有界,所得的全局渐近稳定性的充分性结果改进了相关文献的结论.最后给出了例子及仿真说明充分条件的有效性.Abstract： In this paper,we construct a better Lyapunov function for the nonlinear third order delay system by onlysupposing that the positive half orbit of the system is bounded.The original strong condition is removed,which demands that the Lyapunov function must trend to infinity.The results have improved the conclusions of relevant literatures.At last,examples are given and simulation is made to show the effectiveness of the sufficient conditions. 相似文献