AAM  >> Vol. 5 No. 3 (August 2016)

    一类离散SIR流行病模型的分岔和混沌分析
    Bifurcation and Chaos Analysis of a Class of Discrete SIR Epidemic Models

  • 全文下载: PDF(597KB) HTML   XML   PP.390-398   DOI: 10.12677/AAM.2016.53048  
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作者:  

庞琴,张建刚,邓田,殷俊,卢加荣:兰州交通大学数学学院,甘肃 兰州

关键词:
离散SIR模型Flip分岔Hopf分岔混沌随机参数Discrete-Time SIR System Flip Bifurcation Hopf Bifurcation Chaos Random Parameter

摘要:
本文讨论了离散模型的动力学行为。得到无病平衡点和地方病平衡点的局部稳定性。结果表明,利用中心流形定理和分岔理论,模型存在Flip分岔和Hopf分岔。因此,表现出复杂的动力学行为,这些结果揭示了离散模型的更丰富的动力学行为。

The paper discusses the dynamical behaviors of a discrete-time SI epidemic model. The local sta-bility of the disease-free equilibrium and endemic equilibrium is obtained. It is shown that the model undergoes Flip bifurcation and Hopf bifurcation by using center manifold theorem and bi-furcation theory. So it exhibits the complex dynamical behaviors. These results reveal far richer dynamical behaviors of the discrete epidemic model.

文章引用:
庞琴, 张建刚, 邓田, 殷俊, 卢加荣. 一类离散SIR流行病模型的分岔和混沌分析[J]. 应用数学进展, 2016, 5(3): 390-398. http://dx.doi.org/10.12677/AAM.2016.53048

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