Analysis of the geometric characteristic quantity of the periodic solutions of the chaotic oscillator system and the quantitative detection of weak periodic signal

Abstract

We proposed a quantitative detection method for weak periodic signal in this paper. A result is obtained when analyzing the stable output of chaotic oscillator system in the large-scale periodic state, which shows that the average area of the periodic solution of the chaotic oscillator system is a steady geometric characteristic quantity of periodic solutions of the chaotic oscillator system. There is a steadily and monotonically increasing relation between the average area and the amplitude to be detected. When some parameters are defined, the precision of the geometric characteristic quantity can reach 10-6V2. The further quantitative detection of weak signals is built based on the two characteristics of the chaos system, namely the immunity to noise and sensitivity to weak signal. The simulation experiments shown that the immunity to noise will be enhanced along with the increase of amplitude detected while the precision can be guaranteed.