Emergent excitability in adaptive networks of non-excitable units

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 adaptive networks of globally coupled non-excitable units. The ingredients to observe collective excitability are the coexistence of states with different degree of synchronizaton 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.

6 pages, 5 figures

References in corpus (4)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Macroscopic description for networks of spiking neurons
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Hysteretic transitions in the Kuramoto model with inertia

Cited by in corpus (5)

• Recurrent chaotic clustering and slow chaos in adaptive networks
• Collective excitability in highly diluted networks of rotators
• Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
• Modelling power grids as pseudo adaptive networks
• Type-III intermittency in emergent bursting dynamics of globally coupled rotators