Non-symmetric interactions trigger collective swings in globally ordered systems

TL;DR

This paper demonstrates that non-symmetric interactions and local heterogeneities in biological and social systems lead to persistent collective state changes, contrasting with the stability seen in physical systems, and explains observed behaviors in animal groups.

Contribution

It reveals how non-symmetric interactions and network heterogeneities cause ongoing collective fluctuations, providing a new understanding of stability differences between biological and physical systems.

Findings

Non-symmetric interactions amplify noise effects.

Local heterogeneities localize fluctuation modes.

System exhibits finite relaxation time regardless of size.

Abstract

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable than their physical analogues and spontaneously change their global state on relatively short timescales. In this paper we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state: the non-symmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. The consequences of these features can be larger the larger the system size leading to a localization of the fluctuation modes and a relaxation time that remains finite in the thermodynamic limit. The system keeps changing its global state in time, being constantly driven out of equilibrium by spontaneous fluctuations. Our results explain what is observed in several living and social systems and are consistent with recent experimental data on bird flocks and other animal groups.