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

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