共查询到19条相似文献,搜索用时 109 毫秒
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具有非线性传染率的两类传染病模型的全局分析 总被引:6,自引:1,他引:5
讨论了两类带有非线性传染率的SIS型和SIRS型传染病模型,得到了各类平衡点存在的阈值条件。借助构造Dulac函数和Liapunov函数,找到了各类平衡点全局渐近稳定的充要条件。 相似文献
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本文研究了一类具有饱和发生率的离散SIR传染病模型的动力学性态.我们利用再生矩阵的方法定义了模型的基本再生数;直接计算得到了平衡点的存在性;利用线性化矩阵和Jury判据讨论了平衡点的稳定性;利用中心流形定理讨论了平衡点处可能发生的分支,包括flip分支和Hopf分支.最后,通过数值模拟展示了所得到的理论结果和模型的复杂动力学性态. 相似文献
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考虑到年龄在一些传染病流行过程中的重要影响,建立了一个具有一般传染率的 SIRS 年龄结构仓室模型。通过将模型改写为抽象柯西问题并利用 Hille-Yosida 算子相关定理,分析了模型的动力学性态,讨论了平衡点的稳定性以及平衡点失稳时产生 Hopf 分支的条件。结果表明,当基本再生数小于 1 时,免疫年龄不影响无病平衡点的全局稳定性;当基本再生数大于 1 时,免疫年龄扰动导致地方病平衡点的稳定性改变,从而产生 Hopf 分支。同时,数值模拟验证了理论结果并显示了免疫年龄对模型动力学性态的影响。 相似文献
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捕食者有病的生态-流行病SIS模型的分析 总被引:10,自引:0,他引:10
建立并分析了捕食者具有疾病的生态一流行病SIS模型,讨论了解的有界性。应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步,分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。 相似文献
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R. S. Guttalu H. Flashner 《International journal for numerical methods in engineering》1988,26(4):875-890
The backward mapping approach for computation of global domains of attraction of asymptotically stable non-critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approach. 相似文献
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Fotis A. Papoulias Michael M. Bernitsas 《Dynamical Systems: An International Journal》1986,1(4):323-341
The stability in the sense of Liapunov of the horizontal plane slow motions of Single Point Mooring (SPM) systems is studied. The mathematical model consists of the manoeuvering equations of the moored vessel and a nonlinear stress-strain relation for the mooring line. Steady excitation from current, wind and drift forces is included. Six first-order nonlinear coupled differential equations describe the system dynamics The system equilibria are first found and local analysis is performed in their vicinity. A SPM system, may asymptotically converge to a stable equilibrium, diverge from an unstable equilibrium or converge to a limit cycle. Due to the dependence of the eigenvalues of the system at each equilibrium on the system, parameters, the system may exhibit codimension-one bifurcations of pitchfork or Hopf type, or bifurcations of closed orbits. Based on the results of local analysis, the global system behaviour can be assessed, and design decisions can be made for selection of the principal SPM configuration parameters to avoid undesirable response. Finally the large-amplitude low-frequency motions observed in moored vessels, and often attributed to time-dependent external excitation, are explained using the results of the stability analysis. 相似文献
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预防接种情况下非线性饱和接触率SIR流行病模型动力学性态研究 总被引:2,自引:1,他引:2
研究了一类预防接种情况下具有一般非线性饱和接触率SIR流行病模型动力学性态。得到决定疾病灭绝和持续生存的基本再生数。当基本再生数小于等于1时,仅存在无病平衡态:当基本再生数大于1时,除存在无病平衡态外,还存在惟一的地方病平衡态。利用Hurwitz判据、Liapunov-Lasalle不变集原理得到各个平衡态局部渐近稳定及无病平衡态全局渐近稳定的条件。特别地。当传染率为双线性时,无病平衡态及地方病平衡态全局渐近稳定。 相似文献
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研究了非线性弱最小相位系统的状态反馈全局镇定问题 .在无通常要求被驱动系统全局渐近稳定的情况下 ,提出了若干全局可镇定的充分条件 .一个例子说明了本文结果的适用性 相似文献
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:研究一类具有一般形式非线性饱和传染率染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值条件——基本再生数。当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐遗稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在。已有的两类模型可视为本模型的特例,其相关结论可作为本文的推论。 相似文献