| 带有线性反馈的随机Mathieu-duffing系统的分岔 |
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| 引用本文： | 张冬梅.带有线性反馈的随机Mathieu-duffing系统的分岔[J].辽宁工程技术大学学报(自然科学版),2012,31(1):135-138. |
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| 作者姓名： | 张冬梅 |
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| 作者单位： | 临沂大学理学院,山东临沂,276005 |
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| 基金项目： | 山东省自然科学基金资助项目(Y2007A17);山东省优秀青年教师国内访问学者基金资助项目 |
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| 摘 要： | 为了解决参数激励下带有两个时滞参数的随机Mathieu-duffing系统的主参数共振分岔控制问题,采用用多尺度方法分离参数系统的快慢变量,推导出该时滞动力系统的分岔响应方程,分析时滞参数对系统主共振分岔的影响,讨论方程所有解的情况;利用奇异性理论分析系统发生极限点分岔的条件.研究结果表明:时滞项的系数、时滞参数、调谐参数对系统分岔具有控制作用.
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| 关 键 词： | 随机Mathieu-duffing系统 时滞 调谐参数 主共振 多尺度法 分岔控制 时滞动力系统 奇异性 |
Bifurcation control of stochastic Mathieu-duffing system with linear feedback |
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| ZHNAG Dongmei.Bifurcation control of stochastic Mathieu-duffing system with linear feedback[J].Journal of Liaoning Technical University (Natural Science Edition),2012,31(1):135-138. |
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| Authors: | ZHNAG Dongmei |
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| Institution: | ZHNAG Dongmei(College of Mathematics,Linyi University,Linyi 276005,China) |
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| Abstract: | This study is to solve the bifurcation control with principal parametric resonance of Mathieu-duffing equation under a narrow-band random excitation with two time-delays.The method of multiple scales is used to derive the equations of modulation of amplitude and phase.The bifurcation can be affected by the time delays.The study discusses the bifurcation equation based on singularity theory.Therefore,the effect of time delays on the steady response can be found. |
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| Keywords: | stochastic Mathieu-duffing system time delays tuning parameter primary parametrical resonance the method of multiple scales bifurcation control dynamics of nonlinear systems involving time delays singularity theory |
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