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有界噪声激励下带有时滞反馈的随机Mathieu-Duffing系统的响应
  • ISSN号：1000-3290
  • 期刊名称：《物理学报》
  • 时间：0
  • 分类：O175.1[理学—数学;理学—基础数学] TP13[自动化与计算机技术—控制科学与工程;自动化与计算机技术—控制理论与控制工程]
  • 作者机构：[1]西北工业大学应用数学系,西安710072, [2]佛山大学数学系,佛山528000
  • 相关基金：国家自然科学基金（批准号：10872165）资助的课题.
作者： 邢真慈[1], 徐伟[1], 戎海武[2], 王宝燕[1]
关键词： 随机Mathieu-Duffing系统, 多尺度, 稳定性, 分岔, stochastic Mathieu-Duffing system, multiple scales, stability, bifurcation
中文摘要：

研究了参数激励下带有时滞反馈的随机Mathieu-Duffing方程的主参数共振响应问题.运用多尺度方法分离了系统的快慢变量.分析了系统的分岔性质,发现调谐参数、时滞、时滞项的系数以及非线性项的强度等都可以影响系统的分岔行为,适当选择这些参数可以改变系统的分岔响应.同时,还讨论了非零解的稳定性,得到了非零解稳定的充要条件,而且发现在随机激励的带宽较小时,系统的多解现象仍然存在,分岔和跳跃现象仍会发生,数值模拟验证了理论推导的有效性.

英文摘要：

We investigate the principal parametric resonance of Mathieu-Duffing Equation under a narrow-band random excitation with time delay feedback. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The bifurcation of the system is discussed. We find that the bifurcation can be influenced by the detuning parameter, time delay, and the intensity of the non-linear term, and an appropriate choice of these parameters can change the response of bifurcation. In addition the stability of nontrivial solution is studied. The nontrivial solution of necessary and sufficient condition for stability is obtained. Moreover, we find that when the bandwidth of the random excitation is smaller, the multi-solution phenomenon still exists, and bifurcation and jumping phenomenon will occur. Theoretical analysis is verified by numerical results.

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期刊信息
  • 《物理学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国物理学会 中国科学院物理研究所
  • 主编：欧阳钟灿
  • 地址：北京603信箱(中国科学院物理研究所)
  • 邮编：100190
  • 邮箱：apsoffice@iphy.ac.cn
  • 电话：010-82649026
  • 国际标准刊号：ISSN：1000-3290
  • 国内统一刊号：ISSN：11-1958/O4
  • 邮发代号:2-425
  • 获奖情况:
  • 1999年首届国家期刊奖,2000年中科院优秀期刊特等奖,2001年科技期刊最高方阵队双高期刊居中国期刊第12位
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  • 被引量:49876