Investigation On Self-Organized Critical Behavior Of Earthquake Model On Complex Networks

We introduce the basic concept and the principle of self-organized criticality, several typical mechanism models on complex network, and its typical model-earthquake model. We summarize the structure, driving mechanism, toppling rules, avalanche dynamics and the newest investigation of some main earthquake models. On this base, we establish two new earthquake models with different driving mechanisms and spatial topology, and we use numerical simulation, study in detail the critical scaling behavior and avalanche dynamics of these models, we get some innovative and valuable conclusion. Furthermore, we compare and analyze the obtained results with the relative results on the international literature; this is not only helpful to the study on earthquake model, but also useful to the whole investigation on self-organized criticality in complex system.First, we consider the influence of the inhomogeneity on the critical behavior in the one variable earthquake model on random network. Our numerical study shows that, the critical behavior of the system is very sensitive to the inhomogeneity, different inhomogeneities can result in different critical behavior. More exactly, the two models which have the same nearest neighbors and dissipative parameters, but have different inhomogeneities are not in the same universality class.Second, we establish the one variable earthquake model on the random network which the energy redistributed randomly. Our numerical study shows that: the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys simply finite size scaling. Furthermore, when the system is conservative, different spatial topologies don't alter the critical behavior of the system. Whereas, when the system is nonconservative, the model does not display scaling behavior.At last, we establish the two-variable earthquake model on the random network. We numerically study the critical behavior of the model: we find that our model exhibits self-organized critical deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. Different spatial topologies don't alter the critical behavior of the system. In addition, a power law relation between the size and the duration of an avalanche exists, providing further evidence of criticality in the conconservative system.Our results show that different spatial topologies don't alter the critical behavior of the system, but different inhomogeneities(this corresponds to different boundary conditions in the OFC model on a lattice), toppling rules and driving mechanisms alter the behavior of the system significantly and change the universality class of models.