Coupling-induced resonance in two mutually and asymmetrically coupled oscillators

We consider two mutually coupled oscillators, where we have independent control over the magnitude, sign, and delay of the coupling signal. For appropriate tuning of the coupling constants, there is a coupling-induced resonance where the amplitude becomes large. We investigate the role of nonlinear dissipation and amplitude-dependent frequency correction on the coupling resonance. With delayed coupling, we track the deformation of the resonant bifurcation equation through imperfect bifurcations and the generation of isolas, which generate intervals of multistability between oscillations of different amplitudes. The resonance should be observable in coupled-oscillator systems, where the amplitude remains an important dynamical variable, but not in limit-cycle oscillators modeled by phase-only descriptions.