非线性解的多种成份及其特征  

The Multi-components of Nonlinear Solutions and Its Characteristics

作　　者：黄炳华[1] 周珊[1] HUANG Binghua;ZHOU Shan(Electrical Engineering School of Guangri University,Nanning,530004,CHN)

机构地区：[1]广西大学电气工程学院

出　　处：《固体电子学研究与进展》2019年第6期436-443,共8页Research & Progress of SSE

基　　金：国家自然科学基金资助项目(60662001)

摘　　要：非线性动态电路完全响应的全过程,包含各种各样成份,它们是相互耦合在一起,不能单独分开求解而后迭加。按线性电路的分析方法,完全响应又能划分成自然分量和受迫分量。非线性自然分量包含有未进入稳态振荡前的暂态分量与进入稳态的自激振荡分量。对于不同的起始条件,有不同的暂态过程和稳态自振分量。自振荡形状的巨大变化有时非常敏感的依赖于初始值的微小变化即蝴蝶效应。非自治电路的自振荡分量和受迫振荡分量耦合在一起构成总的稳态振荡,可用谐波分析法和功率平衡定理求出两分量相互耦合的主谐波解。如果在仿真时间内,三阶自治电路的自然解或二阶非自治电路的耦合解,还无法形成闭合的周期轨,也就无法区分暂态与稳态,相图中轨线的缠绕非常密集,从而形成混沌振荡。The complete response of the whole process of nonlinear dynamic circuit contains various components.They are mutual coupling together,cannot be solved alone and superposition afterward.The complete response also can be divided into natural and forced components via analysis method of linear circuit.The nonlinear natural components contain transient processes before entering steady state oscillation and steady state self-excited oscillation.For different initial condition,there are different transient processes and steady state self-oscillation components.The tremendous variation of self-oscillation depend sometime very sensitively on tiny variation of initial condition namely butterfly effect.The coupling of the self-oscillation and forced-oscillation components constitutes overall steady state oscillation in non-autonomous circuit.The main harmonic of the coupling solutions can be found by means of the harmonic analysis method and power balance theory.If within simulation interval,the third order natural solutions of the autonomous circuit or the second order coupling solutions in non-autonomous circuit cannot form the close orbit,the transient processes and steady state oscillation cannot be distinguished,and the trajectory in the phase portrait is very dense,thereby the chaos is formed.

关 键 词：非线性解 自然解 自激振荡 受迫振荡 不稳定平衡态 混沌 

分 类 号：TN572[电子电信]