Analysis of unstable periodic solution of nonlinear circuits using Haar wavelet transform

It has been reported that unstable periodic solution of a dynamical systems make the chaos control easier. But it is difficult to find unstable periodic solution because of a few numerical errors in numerical calculations. Therefore, in this study, we find unstable periodic solution using Haar wavelet transform. Haar wavelet can be easily treated and differential and integral operator matrices are easily derived by using a block pulse function. Therefore it can be adapted to time variable circuit and nonlinear circuit. Furthermore, it can analyze a range of the singular point neighborhood more precisely. In this paper, we show the method to find unstable periodic solution of the autonomous nonlinear circuit using an oscillator with 5th-power nonlinear order characteristic and prove that it is possible to find unstable periodic solution.