  Non-autonomous perturbations of isochronous systems in the plane are
considered. It is assumed that the intensity of perturbations decays with time,
and the frequency is asymptotically constant with the limiting value satisfying
a resonance condition. We discuss the emergence of attracting resonant
solutions with an asymptotically constant amplitude. By combining the averaging
technique and the Lyapunov function method, we show that this behaviour can
occur in the phase locking and phase drifting regimes. The conditions that
guarantee the existence and stability of such resonant dynamics are described.
