A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises)
12 Pages Posted: 16 Nov 2017
Date Written: October 31, 2017
We analyse 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 endogenised 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 thorough analysis of chaotic behaviour, 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.
Keywords: Ising model, dynamic map, social opinion dynamics, bifurcation diagram, chaos, regime shifts, bifurcation delay
JEL Classification: C32, G01, C73
Suggested Citation: Suggested Citation