Two families of super-harmonic resonances in a time-delayed nonlinear oscillator

摘要: Abstract Two stable bifurcating periodic solutions are numerically found to coexist in a time-delayed nonlinear oscillator by using different initial conditions, after the trivial equilibrium loses its stability via two-to-one resonant Hopf bifurcations. These two coexisting have amplitudes and frequency components with one having frequencies of bifurcations while other containing from those The dynamic interaction excitation can induce families super-harmonic resonances, when forcing is approximately at half lower component solutions. It that forced response under resonances exhibits qualitatively behaviour. In addition, family may suddenly disappear magnitude reaches certain value then becomes non-resonant response. be established adjusting accordingly. Time trajectories, phase portraits, spectra, basin attraction bifurcation diagrams given characterise behaviours oscillator.