Self-organized bistability on globally coupled higher-order networks

TL;DR

This paper extends the concept of self-organized bistability to higher-order networks embedded in simplicial complexes, revealing its role in transient synchronization phenomena and potential parallels with epileptic brain activity.

Contribution

It develops a theoretical framework for SOB on higher-order networks using Ott-Antonsen reduction, highlighting coupling constraints and validating with numerical simulations.

Findings

SOB requirements derived for higher-order networks match simulations.

Spontaneous synchronized events are crucial for understanding SOB dynamics.

Weak coupling SOB exhibits traits similar to epileptic brain activity.

Abstract

Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.