Simulation and theoretical analysis on detection of the frequency of weak harmonic signals based on a special chaotic system

Abstract

In order to study a kind of chaotic system which is based on the special Duffing-Homes equation, and use it to detect the unknown frequency of weak harmonious s ignals, we prove the existence of the periodic solution and the exclusivism of the solution, carry out simulation experiments to detect harmonious frequency us ing the periodic trajectory of a stable phase state.We also compute the detectio n error |Δω|,when the damping ratio (α) changes and the frequency changes fro m 1Hz to 200Hz. The results show that we have to choose the value of α correspo nding to the different range of frequency by simulation experiments.