Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources

Abstract

We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.

Perspectives on adaptive dynamical systems

“…38 Another active branch of research concerns adaptation as a general control mechanism, establishing its role in inducing critical transitions 30,31 and triggering of alternating or cyclic activity patterns. [39][40][41] Moreover, unfolding studies employing reservoir computing for design of controllers for nonlinear, and, in particular, chaotic systems, also hold great promise; see Sec. IV C.…”

“…34,35 Apart from understanding the impact on synchronization problems, an important issue concerns the role of adaptation in inducing cyclic activity patterns by controlling critical transitions of the adaptation-free system. Treating such problems, such as the onset of collective activity bursts in heterogeneous systems adaptively coupled to a pool of resources, 39 requires combining different reduction approaches [50][51][52] and multiple timescale methods. Nevertheless, developing rigorous mathematical approaches where mean-field methods apply to layer dynamics while adaptation is treated by a reduced system is a vibrant field of investigation.…”

Asymmetric adaptivity induces recurrent synchronization in complex networks

“…This phenomenon of activity bursting has been also reported in a population of excitable units adaptively coupled to a pool of resources. 36 In a broader sense, the mechanism for recurrent synchronization, which we report here, is based on a recurrent slow dynamics of hidden variables that we relate to adaptive coupling weights between dynamical populations in this work. When adaptation is heterogeneous (asymmetric), the hidden variables lead to reemergence of episodes of synchronization and desynchronization.…”