Coexistence of two families of sub-harmonic resonances in a time-delayed nonlinear system at different forcing frequencies

Two coexisting families of sub-harmonic resonances can be induced at different forcing frequencies in a time-delayed nonlinear system having quadratic nonlinearities. They occur in the region where two stable bifurcating periodic solutions coexist in the corresponding autonomous system following two-to-one resonant Hopf bifurcations of the trivial equilibrium. The forced response is found to demonstrate small- and large-amplitude quasi-periodic...