带有双噪声的随机SI传染病模型的稳定性与分岔

赵金庆; 刘茂省; 马扬军; 王弯弯

doi:10.3879/j.issn.1000-0887.2013.12.009

带有双噪声的随机SI传染病模型的稳定性与分岔

doi: 10.3879/j.issn.1000-0887.2013.12.009

中北大学理学院, 太原 030051

基金项目: 国家自然科学基金资助项目(10901145)；山西省自然科学基金资助项目(20120110021)；山西省高等学校优秀青年学术带头人资助项目

详细信息

作者简介:
赵金庆(1988—),男，山东淄博人，硕士生(E-mail: qing630086824@126.com);刘茂省(1978—)，男，山东济宁人，副教授，博士(通讯作者. E-mail: liumxsx@gmail.com).

中图分类号: O29;O175.13
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出版历程
- 收稿日期: 2013-05-27
- 修回日期: 2013-08-28
- 刊出日期: 2013-12-16

Stochastic Stability and Bifurcation of an SI Epidemic Model With Double Noises

Department of Mathematics, North University of China, Taiyuan 030051, P.R.China

Funds: The National Natural Science Foundation of China(10901145)

摘要

摘要: 建立一个带有双噪声的随机SI传染病模型，运用随机平均法及非线性动力学理论对模型进行化简．通过Lyapunov指数和奇异边界理论，得到模型的局部随机稳定性和全局随机稳定性的条件．根据不变测度的Lyapunov指数和平稳概率密度，分析模型的随机分岔．结果表明，系统在随机因素作用下变得更敏感、更不稳定.
- 随机平均法 /
- Lyapunov指数 /
- 不变测度 /
- 随机稳定 /
- 随机分岔
Abstract: A stochastic SI epidemic model was proposed with double noises. With the stochastic averaging method and nonlinear dynamic theory, the SI epidemic model was simplified. According to the Lyapunov exponent and singular boundary theory, some new criteria ensuring the model’s local and global stochastic stability were obtained. By dint of the Lyapunov exponent of invariant measure and the stationary probability density, the stochastic bifurcation of the model was explored. Results show that the system under the effect of random factors becomes more sensitive and more unstable.
- stochastic averaging method /
- Lyapunov exponent /
- invariant measure /
- stochastic stability /
- stochastic bifurcation

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参考文献(16)

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