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We study a system of dynamical units, each of which shows excitable oroscillatory behavior, depending on the choice of parameters. When we couplethese units with repressive bonds, we can control the duration of collectiveoscillations for an intermediate period between collective fixed-pointbehavior. The control mechanism works by monotonically increasing a singlebifurcation parameter. Both the onset and arrest of oscillations are due tobifurcations. Depending on the coupling strength, the network topology and thetuning speed, our numerical simulations reveal a rich dynamicsout-of-equilibrium with multiple inherent time scales, long transients towardsthe stationary states and interesting transient patterns like self-organizedpacemakers. Zooming into the transition regime, we pursue the arrest ofoscillations along the arms of spirals. We point out possible relations to thegenetic network of segmentation clocks.

A simple mechanism for controlling the onset and arrest of collective oscillations in genetic circuits