A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises)

Damian Smug, Didier Sornette and Peter Ashwin
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Damian Smug: University of Exeter
Didier Sornette: ETH Zurich and Swiss Finance Institute
Peter Ashwin: University of Exeter

No 17-34, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C32 C73 G01 (search for similar items in EconPapers)
Pages: 12 pages
Date: 2017-11
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1734

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