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力学学报  2014 

受周期和白噪声激励的分段线性系统的吸引域与离出问题研究

DOI: 10.6052/0459-1879-13-300, PP. 447-456

Keywords: 分段线性系统,离出问题,平均首次通过时间

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Abstract:

离出行为是随机非线性系统的重要现象之一,而离出问题是除随机动力系统理论以外考察随机非线性系统随机稳定性的另一种重要的方法.分段线性系统是一个经典的非线性动力学模型,受随机激励后成为随机系统,但并不是严格的随机动力系统,因而此时随机动力系统理论也不适用.为了研究同时受周期和白噪声激励的分段线性系统,首先使用Poincaré截面模拟其在无噪声时确定性的动力学行为,然后使用MonteCarlo模拟对其在白噪声激励下的离出行为进行了数值仿真分析.其次,为了考察离出问题中的重要参数,系统的平均首次通过时间(meanfirst-passagetime,MFPT),使用vanderPol变换,随机平均法,奇异摄动法和射线方法进行了量化计算.通过对理论结果与模拟结果的对比分析,得到结论当系统吸引子对应的吸引域边界出现碎片化时,理论结果与模拟结果的误差极大;而当吸引域边界足够光滑的以后,理论结果与模拟结果才会相当吻合.

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