| 二阶非线性电路中的不相容性 |
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| 引用本文： | 徐云,常飞,奎丽荣,张建峡,周红,迟忠君.二阶非线性电路中的不相容性[J].清华大学学报(自然科学版),2005,45(10):1313-1315. |
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| 作者姓名： | 徐云 常飞 奎丽荣 张建峡 周红 迟忠君 |
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| 作者单位： | 清华大学,电机工程与应用电子技术系,电力系统及大型发电设备安全控制国家重点实验室,北京,100084;贵州大学,电工学院,贵阳,550003 |
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| 基金项目： | 国家自然科学基金资助项目(59577025)，清华大学基础研究基金资助项目(JC2001021) |
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| 摘 要： | 为了研究动力学系统和混沌中产生的跳跃随机性,利用能量平衡原理分析了二阶非线性电路的退化方程。发现了动力学系统中的连续不相容性是电路状态发生跳跃的原因之一,这种连续不相容性是指解依约束方程电路的状态轨迹运动进入某一区域时,其任何运动与停止都是与该约束方程相矛盾的:电路状态是处于既不能向前,又不能后退,也不能停止不动的境地,而在该区域外的临近区域,它的运动都与约束方程相容。同时发现动力学系统中的非线性函数项(或非线性元件)能够发生跳跃随机性和产生跳跃随机曲线,以使电路的状态轨迹达到与约束方程相容的状态。
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| 关 键 词： | 动力学系统 不连续性跳跃 连续不相容性 |
| 文章编号： | 1000-0054(2005)10-1313-03 |
| 修稿时间： | 2004年12月15 |
Incompatibility conditions in nonlinear second order circuit |
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| XU Yun,CHANG Fei,KUI Lirong,ZHANG Jianxia,ZHOU Hong,CHI Zhongjun.Incompatibility conditions in nonlinear second order circuit[J].Journal of Tsinghua University(Science and Technology),2005,45(10):1313-1315. |
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| Authors: | XU Yun CHANG Fei KUI Lirong ZHANG Jianxia ZHOU Hong CHI Zhongjun |
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| Institution: | XU Yun~1,CHANG Fei~1,KUI Lirong~1,ZHANG Jianxia~2,ZHOU Hong~1,CHI Zhongjun~1 |
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| Abstract: | Chaos related discontinuity jumps in nonlinear dynamic systems were analyzed using a second order nonlinear circuit model and degenerative equations based on the energy balance principle.The jumps of the circuit state were found to result from the incompatibilities in the dynamic system when the motion trace of the circuit state contradicts the constraint equations as the system enters a new region.The circuit state can then not go forward,can not go backward and can not remain constant.However,the system compatible with the constraint equations near this incompatibility region.The analysis also shows that the nonlinear terms in the dynamic system equations cause the stochastic state to jump so that the circuit state can reach compatibility with the constraint equations. |
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| Keywords: | dynamics system discontinuity jump continuous incompatibility properties |
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