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非线性局部Lyapunov指数方法在目标观测中的应用初探

刘德强 丁瑞强 李建平 冯杰

刘德强, 丁瑞强, 李建平, 冯杰. 非线性局部Lyapunov指数方法在目标观测中的应用初探[J]. 大气科学, 2015, 39(2): 329-337. doi: 10.3878/j.issn.1006-9895.1405.13337
引用本文: 刘德强, 丁瑞强, 李建平, 冯杰. 非线性局部Lyapunov指数方法在目标观测中的应用初探[J]. 大气科学, 2015, 39(2): 329-337. doi: 10.3878/j.issn.1006-9895.1405.13337
LIU Deqiang, DING Ruiqiang, LI Jianping, FENG Jie. Preliminary Application of the Nonlinear Local Lyapunov Exponent to Target Observation[J]. Chinese Journal of Atmospheric Sciences, 2015, 39(2): 329-337. doi: 10.3878/j.issn.1006-9895.1405.13337
Citation: LIU Deqiang, DING Ruiqiang, LI Jianping, FENG Jie. Preliminary Application of the Nonlinear Local Lyapunov Exponent to Target Observation[J]. Chinese Journal of Atmospheric Sciences, 2015, 39(2): 329-337. doi: 10.3878/j.issn.1006-9895.1405.13337

非线性局部Lyapunov指数方法在目标观测中的应用初探

doi: 10.3878/j.issn.1006-9895.1405.13337
基金项目: 国家重点基础研究发展计划(973计划)项目2012CB955200, 国家自然科学基金项目41175069、41375110

Preliminary Application of the Nonlinear Local Lyapunov Exponent to Target Observation

  • 摘要: 本文初步探讨了非线性局部Lyapunov指数方法(NLLE)在目标观测中的应用。首先, 在NLLE理论基础上研究了非线性动力系统内局部平均误差相对增长(LAGRE)特征, 证明了在误差发展进入随机状态前, LAGRE与初始误差大小无关而是与初始状态有关;在演化进入随机状态后, LAGRE的饱和值由初始误差大小决定这一特征。同时利用三个变量的常微分方程模型Lorenz63验证了这一结论。其次, 从非线性局部误差增长理论出发, 在局部动力演化相似方法(LDA)的基础上提出向前局部动力演化相似方法(FLDA)的概念, 并通过两个混沌个例来说明LDA和FLDA方法能够有效的利用历史资料还原任意初始状态的LAGRE。这些方法的提出为NLLE理论应用于观测资料研究目标观测问题提供了依据。
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  • 收稿日期:  2013-12-20
  • 修回日期:  2014-05-27

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