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We investigate the relation between the dynamics of a single oscillator withdelayed self-feedback and a feed-forward ring of such oscillators, where eachunit is coupled to its next neighbor in the same way as in the self-feedbackcase. We show that periodic solutions of the delayed oscillator give rise tofamilies of rotating waves with different wave numbers in the correspondingring. In particular, if for the single oscillator the periodic solution isresonant to the delay, it can be embedded into a ring with instantaneouscouplings. We discover several cases where stability of periodic solution forthe single unit can be related to the stability of the corresponding rotatingwave in the ring. As a specific example we demonstrate how the complexbifurcation scenario of simultaneously emerging multi-jittering solutions canbe transferred from a single oscillator with delayed pulse feedback tomulti-jittering rotating waves in a sufficiently large ring of oscillators withinstantaneous pulse coupling. Finally, we present an experimental realizationof this dynamical phenomenon in a system of coupled electronic circuits ofFitzHugh-Nagumo type.

Embedding the dynamics of a single delay system into a feed-forward ring