Self-organized criticality and partial synchronization in an evolving network

Abstract

We describe an evolving network type model of stock market, and present numerical results. Recent works on Self-organized criticality in pulse coupled relaxation oscillators have shown SOC to be related to frustrated attempts of the system to synchronise. Other works have shown the emergence of a self-organized control parameter which feeds back onto an order parameter, causing avalanches which separate periods of stasis. We define an all-to-all network of connected spins which also have an attached fitness. We find a self-organized fitness threshold given by the mean fitness, which separates a solid type state from a gaseous type state. We also find a self-organized control parameter given by the fitness deviation. Approach of this parameter to zero causes `avalanches' of partial synchronizations which occur on all sizes, separated by periods of stasis, and re-order the system.