Periodic and Chaotic Motion of a Time-Delayed Nonlinear System Under Two Coexisting Families of Additive Resonances

A time-delayed quadratic nonlinear mechanical system can exhibit two coexisting stable bifurcating solutions (SBSs) after two-to-one resonant Hopf bifurcations occur in the corresponding autonomous time-delayed system. One SBS is of small-amplitude and has the Hopf bifurcation frequencies (HBFs), while the other is of large-amplitude and contains the shifted Hopf bifurcation frequencies (the shifted HBFs). When the forcing frequency is tuned to...