Emergent excitability in adaptive networks of non-excitable units

TL;DR

This paper demonstrates that adaptive networks of non-excitable units can spontaneously exhibit collective excitability and bursting oscillations due to the interplay of local dynamics and global feedback, with analytical insights provided for Kuramoto models.

Contribution

It reveals how adaptation induces excitability in non-excitable units through global feedback and analyzes the macroscopic dynamics in Kuramoto models with inertia.

Findings

Collective excitability emerges in adaptive non-excitable networks.

Bimodal Kuramoto model exhibits a critical manifold governing dynamics.

Adaptation maintains networks in a permanently out-of-equilibrium state.

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.