Noise-induced volatility of collective dynamics

TL;DR

This paper investigates how intermediate noise levels can cause increased fluctuations in collective bistable systems, leading to uncorrelated responses with external signals, with implications for financial markets, biological systems, and out-of-equilibrium phenomena.

Contribution

It introduces a comprehensive analytical and numerical study of noise-induced volatility in collective dynamics, highlighting its ubiquity and potential applications across various complex systems.

Findings

Noise-induced volatility increases fluctuation levels.

System responses become uncorrelated with external signals at intermediate noise.

The phenomenon is robust across different network topologies.

Abstract

"Noise-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical signature of this phenomenon is that --beyond the increase in the level of fluctuations-- the response of the system becomes uncorrelated with the external driving force, making it different from stochastic resonance. Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of this phenomenon, which is argued to be a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems and of strong selective responses of immune systems of complex biological organisms. Extensive numerical simulations are compared with a mean-field theory for different network topologies.