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Abstract |
Population bursts in a large ensemble of coupled elements result from the
interplay between the local excitable properties of the nodes and the global
network topology. Here, collective excitability and self-sustained bursting
oscillations are shown to spontaneously emerge in globally coupled populations
of nonexcitable units subject to adaptive coupling. The ingredients to observe
collective excitability are the coexistence of states with different degrees of
synchronization joined to a global feedback acting, on a slow timescale, against
the synchronization (desynchronization) of the oscillators. These regimes are
illustrated for two paradigmatic classes of coupled rotators, namely, the
Kuramoto model with and without inertia. For the bimodal Kuramoto model we
analytically show that the macroscopic evolution originates from the existence
of a critical manifold organizing the fast collective dynamics on a slow
timescale. Our results provide evidence that adaptation can induce excitability
by maintaining a network permanently out of equilibrium.
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