Noise-induced volatility of collective dynamics

Georges Harras, Claudio J. Tessone, Didier Sornette

Published 2010-04-13, updated 2011-08-09Version 2

"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.