#Self-Organized Criticality

Self-organized criticality (SOC) is a property of nonlinear dynamical systems that have a critical point as an attractor… meaning the system is structured in such a way that it organizes itself into a critical state. Many small local interactions that have no global effect build up to a critical point… resulting in a very large global event occurring. Phenomena that are a product of SOC exhibit a power law distribution in the frequency of their occurrence. Meaning the system’s development follows a pattern of many many small events happening and then a very very large event flowing when the system reaches the critical point. The sandpile model was the first model to exhibit self-organized critical behavior, where the system endogenously moves towards its critical (phase transition) point. when we drop small grains (of something like sand) on top of each other they will build up into a pile with occasional grains running off, one or two at a time, in proportion to the rate at which we are dropping them, this is the linear equilibrium state to the system’s development, grains of sand are held on the pile by its low incline and the friction from other grains that have already built up (this is the attractor). But at some critical point the pile of sand has built up to such an extent that the incline on the side has reached a critical level, by dropping just one additional grain of sand we can cause a cascading avalanche, a positive feedback as each new grain of sand that cascades down destabilizes the system more which will feedback to effect more grains to slide off. here we can note the prolonged period for which the system was held in a stable equilibrium and the very short period of rapid nonlinear change, this is also an illustration of the idea of punctuated equilibrium. The tragedy of the commons is a generalization of SOC Because it is the way that the parts are incentivised to act local that leads to a global critical point and collapse. Many individual small events where it is individually rational to take actions that create very small negative externalities. Which ultimately build up to a critical global state resulting in a very large nonlinear event. This phenomenon of self-organized criticality has been identified in many different systems from From the occurrence of solar flares To earthquakes to ecological evolution Neuronal Avalanches in the brain to outbreaks of epidemics to fluctuations within financial markets

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