Synchronisation vs. resonance: Isolated resonances in damped nonlinear oscillators

We use bifurcation continuation to compute resonance tongues in the plane of the forcing frequency vs. the forcing amplitude for different but fixed values of the damping rate. Our analysis shows that identified here isolated resonances explain the intriguing “intermingled tongues” that were observed for weak damping and misinterpreted as (synchronisation) Arnold tongues in Paar and Pavin (1998). What is more, isolated resonances link “intermingled tongues” to a seemingly unrelated phenomenon of “bifurcation superstructure” described for moderate damping in Parlitz and Lauterborn (1985).