富分叉集广义二维动态平均场Ising模型(启发并应用于金融危机)

D. Smug, D. Sornette, P. Ashwin
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引用次数: 9

摘要

我们分析了一个扩展版本的动态平均场Ising模型。该模型描述了交易员的意见动态,而不是经典的自旋和外部磁场的物理表示。外场内化以表示过去状态变量的平滑移动平均值。这个模型在一个简单的设置中捕获了即时社会模仿和过去社会协调趋势之间的相互作用。我们展示了丰富的分支集的存在,作为两个参数的函数,量化了瞬时与过去社会意见对状态变量下一个值形成的相对重要性。此外,我们对混沌行为进行了深入的分析,这是在某些参数范围内表现出来的。最后,我们通过分岔曲线考察了几种转变,并研究了如何将它们理解为特定的市场情景。我们发现,从危机中复苏并推动系统回归“正常”所需的修正幅度,往往远远大于导致危机本身的原因的强度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises)
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.
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