Analytical Threshold for Chaos of Piecewise Duffing Oscillator with Time-Delayed Displacement Feedback

Abstract

In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold curve is obtained by calculation and numerical simulation. The accuracy of the analytical result is proved by some typical numerical simulation results, including the local bifurcation diagrams, phase portraits, Poincaré maps, and the largest Lyapunov exponents. The effects of excitation frequency and time delay of the displacement feedback are analytically discussed. It could be found that the critical excitation amplitude will increase obviously with the increase of the excitation frequency, and under the selection of certain parameters, the critical excitation amplitude takes the time delay of 0.58 as the inflection point, which decreases at first and then increases.

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

“…The blue layered dense points on the Poincaré section in figure 13(c) and the irregular distribution of blue points in the q-s plane in figure 13(d) before the cutoff point, indicate that the system is aperiodic. However, the closed red curve on the Poincaré section and the regular red distribution in the q-s plane after the cutoff point, indicate that the system is queai-periodic [47][48][49]. Consequently, transient chaos coexists in the system.…”