Theoretical Models of Self-Organized Criticality (SOC) Systems

摘要: In this chapter 2 of the e-book "Self-Organized Criticality Systems" we summarize classical cellular automaton models, which consist a statistical aspect that is universal to all SOC systems, and physical depends on definition observable. Then derive some general analytical formulations processes, such as exponential-growth model fractal-diffusive model, also have validity for while specific applications observations require additional scaling laws (e.g., astrophysical or geophysical observations). Finally discuss alternative SOC-related, non-SOC as: self-organization (without criticality), forced Brownian motion diffusion, hyper-diffusion Levy flight, nonextensive Tsallis entropy, turbulence, percolation, phase transitions, network chaotic systems. We synthesize metrics specifies observational properties are shared by these processes.