| 带有双噪声的随机SI传染病模型的稳定性与分岔 |
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| 引用本文： | 赵金庆,刘茂省,马扬军,王弯弯.带有双噪声的随机SI传染病模型的稳定性与分岔[J].应用数学和力学,2013,34(12):1300-1310. |
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| 作者姓名： | 赵金庆 刘茂省 马扬军 王弯弯 |
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| 作者单位： | 中北大学 理学院, 太原 030051 |
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| 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 |
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| 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.
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| 关 键 词： | 随机平均法 Lyapunov指数 不变测度 随机稳定 随机分岔 |
| 收稿时间： | 2013-05-27 |
Stochastic Stability and Bifurcation of an SI Epidemic Model With Double Noises |
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| Affiliation: | Department of Mathematics, North University of China, Taiyuan 030051, P.R.China |
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| 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. |
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