by Pablo Sanchez-Martin, Irene Elices, Alicia Garrido-Peña, Carlos Garcia-Saura, Rafael Levi, Francisco B. Rodriguez, Pablo VaronaIn multiple neural systems, networks of bursting neurons generate and coordinate robust sequential rhythms, such as those observed in central pattern generators (CPGs) that control motor activity. In this paper, we combine electrophysiological experiments and biophysical models of the pyloric CPG to investigate cycle-by-cycle coordination resetting in sequential rhythms. In particular, we focus our analysis on the variability constraints of sequence intervals defined by the burst onset and offset time references, which structure the timing of the rhythmic CPG sequence cycle-by-cycle. We identified the conditions under which sequential dynamical invariants emerge as robust relationships between specific intervals within the same cycle, and when such relations reset at each cycle or extend between intervals of consecutive cycles. Our results help understand the mechanisms underlying the autonomous cycle-by-cycle sequential coordination and the relationships between intervals from consecutive cycles when a slow modulatory action establishes a common trend across the rhythm.