Self-organized Criticality In Complex Systems

Self-organized criticality (SOC) is a new theory which wasn't put forward until 1980s.The theory explains the organizational principle of certain extended dissipative dynamical systems. That is, systems which are open, far from equilibrium, and interactional can naturally evolve into a critical state. In the critical state, there are long range interactions, by which each part of the system feels the influence of all the others. A small perturbation can lead a domino effect and even initiate an"avalanche". Critical states are signaled by a power-law distribution (scale invariance) of the frequency-scale statistics. Systems in this state show maximal complexity, evolution, and innovation. By using the Theory of SOC, we study several complex systems, and gain some irradiative result.(1)We investigate several cellular automation (CA) models which exhibit SOC character, design computational algorithms and give simulations. The result shows that all these systems are evolving in the form of SOC. In sand-pile model, the average sand number is 2.09, while in forest model, fire distributions are like fractal trees. (2)We combine GA with SOC and put forward a new genetic algorithm based on SOC. We design mutation operator and extinction operator and also give analysis of convergence. The result shows that in coequal conditions GAs based on evolutionary behavior of SOC outperform Simple genetic algorithms.(3)We study SOC in economic system. Economic system is a typical complex system that in many aspects it shows SOC. We mainly study two aspects: first, by using the Theory of SOC we interpret the extensive scaling behaviors of fluctuant statistics in Chinse Stock Market, and analyze the characteristic of scaling parameters. Furthermore, we make use of correlative parameters of financial time serials and erect up the SOC topological framework of Chinese Stock Market. We find that Shanghai Market's average topological number is 2.2011 while Shenzhen Market is 2.1872. The result shows that Chinses Stock Market did have the characteristic of SOC. By using the Theory of SOC, we can have a reasonable explanation of the complex phenomena of the market.