排除分析法及在电子线路混沌参数分析中的应用

Exclusion Method and Its Application to the Analysis of Chaotic Electronic Circuit

提出了一种新的混沌解析分析方法:排除分析法.其基本思想是任何系统只有4种可能的解的形式,即常数解(平衡解)、周期解、概周期解和混沌解,如果排除了常数解(平衡解)、周期解、概周期解的存在,系统就只有一种可能,即出现混沌解,从而得到系统出现混沌的解析条件.将这一方法成功应用到Van der Pol—Duffing振荡器的分析中,改进了振荡器出现混沌的解析条件,并利用计算机仿真进行验证,表明结果完全正确.通过与Melnikov方法、Hopf分岔方法、不动点理论得到的结果比较发现,本文提出的排除分析法比以往经典的方法更精确,适应范围更为广泛.所提出的排除分析法可以适用于任何维数的自治系统和非自治系统,是一种新的混沌解析分析法.

A new analytical analysis method for chaos ： exclusion method is presented.Its basic idea is that for any systems,there are only four different solution types,that is,constant solutions（equilibrium solutions）,periodic solutions,almost periodic solutions and chaotic solutions.If the parameter ranges corresponding to the solutions except chaotic solutions are excluded,the remaining parameter ranges are only the areas corresponding to chaotic solutions,and then the analytical conditions for the chaotic solutions are obtained.This new method is applied to Van der Pol-Dufing oscillator and new analytical conditions for chaotic solutions are obtained.The conclusions are proved correct by simulation.Compared with the previous results obtained by Melnikov method,Hopf bifurcation method,fixed points theory,the new results are much more accurate and has much better adaptation for different conditions.The exclusion method is adaptive for both autonomous systems and non-autonomous systems with any degrees,it is a new analytical analysis method for chaos.