Chaotifing Duffing-type System with Large Parameter Range Based on Optimal Time-Delay Feedback Control

This report presents a technique of chaotification based on the optimal time-delay feedback that can make a system chaotic with large chaotic parameters range. The bifurcation analysis is done to determine the stability of the time-delay system. An implicit performance index and an optimization strategy are proposed for the time-delay control scheme that can be effectively carried out to obtain the optimal delay time for chaos with best quality. Simulation results of Duffing-type systems show that it is possible to excite the system behaving chaotically while the feedback controls remain small at favorable level. Chaotification performance is further discussed when the excitation frequency and system parameters are widely changed. Results also reveal an interesting phenomenon that the optimal time-delay chaotification can reduce or even eliminates line spectra apparently when the excitation frequency is approximately lower than 8 Hz, which may potentially lead to an application for line spectra reduction of the radiated noise emitted from underwater vehicles.