Open AccessEmerging spectra characterization of catastrophic instabilities in complex systems
Author(s) -
Anirban Chakraborti,
Kiran Sharma,
Hirdesh K. Pharasi,
K. Shuvo Bakar,
Sourish Das,
T. H. Seligman
Publication year - 2020
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/ab90d4
Subject(s) - physics , eigenvalues and eigenvectors , statistical physics , random matrix , instability , spectral line , quantum mechanics
Random matrix theory has been widely applied in physics, and even beyond physics. Here, we apply such tools to study catastrophic events, which occur rarely but cause devastating effects. It is important to understand the complexity of the underlying dynamics and signatures of catastrophic events in complex systems, such as the financial market or the environment. We choose the USA S&P-500 and Japanese Nikkei-225 financial markets, as well as the environmental ozone system in the USA. We study the evolution of the cross-correlation matrices and their eigen spectra over different short time-intervals or ‘epochs’. A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues, mainly around zero. The statistical properties of the emerging spectrum are intriguing—the smallest eigenvalues and the shape of the emerging spectrum (characterized by the spectral entropy) capture the system instability or criticality. Importantly, the smallest eigenvalue could also signal a precursor to a market catastrophe as well as a ‘market bubble’. We demonstrate in two paradigms the capacity of the emerging spectrum to understand the nature of instability; this is a new and robust feature that can be broadly applied to other physical or complex systems.