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Moment Lyapunov exponent for three-dimensional system under real noise excitation
  • ISSN号：0253-4827
  • 期刊名称：《应用数学和力学：英文版》
  • 时间：0
  • 分类：O415.5[理学—理论物理;理学—物理] TQ320.662[化学工程—合成树脂塑料工业]
  • 作者机构：[1]State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210014, P. R. China, [2]School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu Province, P. R. China
  • 相关基金：Project supported by the National Natural Science Foundation of China （Nos. 11072107, 91016022, and 11232007）
作者： 李胜宏[1,2], 刘先斌[1]
关键词： Lyapunov指数, 三维系统, 噪声激励, 李雅普诺夫指数, 特征值问题, 实时, 渐近展开, 本征值问题, moment Lyapunov exponent, perturbation method, real noise, diffusion process, Fourier series
中文摘要：

The pth moment Lyapunov exponent of a two-codimension bifurcation system excited parametrically by a real noise is investigated.By a linear stochastic transformation,the differential operator of the system is obtained.In order to evaluate the asymptotic expansion of the moment Lyapunov exponent,via a perturbation method,a ralevant eigenvalue problem is obtained.The eigenvalue problem is then solved by a Fourier cosine series expansion,and an infinite matrix is thus obtained,whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent.Finally,the convergence of procedure is numerically illustrated,and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.

英文摘要：

The pth moment Lyapunov exponent of a two-codimension bifurcation systern excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.

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期刊信息
  • 《应用数学和力学：英文版》
  • 主管单位:交通部
  • 主办单位:上海大学
  • 主编：周哲玮
  • 地址：上海市宝山区上大路99号上海大学122信箱
  • 邮编：200444
  • 邮箱：amm@department.shu.edu.cn
  • 电话：021-66135219 66165601
  • 国际标准刊号：ISSN：0253-4827
  • 国内统一刊号：ISSN：31-1650/O1
  • 邮发代号:
  • 获奖情况:
  • 上海市优秀科技期刊一等奖,中国期刊方阵“双效”期刊
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  • 被引量:541