Fig. 1

Snapshots (\(t=0,1,10,100,1000\)) of oscillator phases \(\theta_{s}^{(f)}(t) \in[0,1)\) with periodic boundary condition (\(s=1,\ldots,200\)) for a typical trajectory issued from a random initial condition, when forcing with a uniform signal \(f(t)=t/\tau\). Clearly, a traveling wave with periodic shape emerges in the far-downstream large time limit (i.e., as s and \(t \to\infty\))