Exclusion Method and Its Application to the Analysis of Chaotic Electronic Circuit
Weijun Wang · Hu'nan Shifan Daxue xuebao. Ziran kexue ban · 2010
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.