Noise-induced periodicity in a frustrated network of interacting diffusions

TL;DR

This paper studies how noise can induce periodic behavior in a complex network of interacting diffusions with conflicting intra- and inter-community interactions, revealing noise-driven oscillations.

Contribution

It demonstrates the phenomenon of noise-induced periodicity in a frustrated network with mixed interaction signs, a novel insight into stochastic collective dynamics.

Findings

Moderate noise can induce periodicity in the system.

The system exhibits no periodic behavior in the zero-noise limit.

Noise can create an attractive periodic law in certain interaction regimes.

Abstract

We investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population interactions are positive; each particle wants to conform to the average position of the particles in its own community. On the other hand, inter-population interactions have different signs: the particles of one population want to conform to the average position of the particles of the other community, while the particles in the latter want to do the opposite. We show that this system features the phenomenon of noise-induced periodicity: in the infinite volume limit, in a certain range of interaction strengths, although the system has no periodic behavior in the zero-noise limit, a moderate amount of noise may generate an attractive periodic law.