| 摘要: |
| 确定的Lorenz系统是描述大气运动规律的重要数学模型，具有深厚的应用背景，被许多学者广泛研究，然而气候环境受突变因素影响，确定的情形无法完全解释大气的运动规律性；基于此，研究了一种基于加法白噪声驱动的随机Lorenz系统的渐进行为，通过恰当的估计证明了系统在参数不受约束条件下存在随机吸收集，进而获得了随机Lorenz系统吸引子的存在性，验证了扰动参数趋于零时，随机Lorenz系统收敛到确定的系统，从而利用上半连续性的相关理论证明了随机吸引子在Hausdorff半距离意义下收敛到全局吸引子，表明Lorenz系统的稳定性不受环境因素，比如海啸、地震等的影响。 |
| 关键词: 随机动力系统 随机Lorenz方程组 随机吸引子 上半连续性 |
| DOI： |
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| Attractors and Their Upper Semi continuity of Stochastic Lorenz System Driven by Additive Noises |
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LIU Gui-fen, ZHAO Wen-qiang
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School of Mathematics and Statistics, Chongqing Technology and Business University,Chongqing 400067, China
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| Abstract: |
| The deterministic Lorenz system is an important mathematical model for describing the law of atmospheric motion. It has a profound application background and has been extensively studied by many scholars. However, the climate environment is affected by abrupt factors, and the determined situation cannot fully explain the regularity of atmospheric motion. Based on this, in this paper, we study the progressive behavior of a stochastic Lorenz system driven by additive white noise. We firstly obtain the existence of the random attractor of the random Lorenz system by properly estimating the existence of random absorption set under the condition that the parameters are not constrained. We secondly prove that the stochastic Lorenz system converges to a deterministic system when the perturbation parameter tends to zero. Thirdly, by the theory of the upper semicontinuity, we obtain that random attractor converges to the global attractor in the sense of Hausdorff half distance. This indicates that the stability of the Lorenz system is not affected by environmental factors such as tsunamis, earthquakes, etc. |
| Key words: stochastic dynamical system stochastic Lorenz system random attractor upper semicontinuity |
