Paper Info
Title
A Generalized 2d-Dynamical Mean-Field Ising Model With A Rich Set Of Bifurcations (Inspired And Applied To Financial Crises)
Abstract
We analyze an extended version of the dynamical mean-field Ising model. Instead of classical physical representation of spins and external magnetic field, the model describes traders' opinion dynamics. The external field is endogenized to represent a smoothed moving average of the past state variable. This model captures in a simple set-up the interplay between instantaneous social imitation and past trends in social coordinations. We show the existence of a rich set of bifurcations as a function of the two parameters quantifying the relative importance of instantaneous versus past social opinions on the formation of the next value of the state variable. Moreover, we present a thorough analysis of chaotic behavior, which is exhibited in certain parameter regimes. Finally, we examine several transitions through bifurcation curves and study how they could be understood as specific market scenarios. We find that the amplitude of the corrections needed to recover from a crisis and to push the system back to "normal" is often significantly larger than the strength of the causes that led to the crisis itself.
Year
DOI
Venue
2018
10.1142/S0218127418300100
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Ising model, social opinion dynamics, chaos, regime shifts, bifurcation delay
Journal
28
Issue
ISSN
Citations 
4
0218-1274
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Damian Smug100.34
Didier Sornette223837.50
P. Ashwin3178.26