Quasi-periodic Attributes In The Self-organized Critical State Seismic Model

The natural world of human life is full of phenomenon with scale-free characteristics of time or space.This paper focuses on two kinds of phenomena:self-organized critical earthquake model and fractal.The main research of this paper consists of three parts as follows:First we study the dynamic mechanism of quasi-periodic behavior in self-organized critical earthquake model.In the study of earthquakes,the most famous earthquake model is the OFC model proposed by Olami,Feder and Christensen in 1992.The OFC model showed the existence of self-organized criticality in non-conservative systems.Since then,the model has attracted wide attention.And several extended models are proposed according to the model.In 2006,Ramos,Altshuler and Mal(?)y introduced two variations in the OFC model:(1)Energy threshold of each block in the network was distributed randomly a Gaussian distribution of standard deviation ?.(2)Instead of assuming infinitely accurate tuning,a quantum force was added in each step,keeping the separation of time scales which is more realistic.They found that there were quasi-periodic events in the earthquake model.The period decreased as the degree of dissipation increased.In order to analyze the dynamic mechanism of the quasi-periodic events,we study the dynamic process of collapse of each block in the network.We analyze the characteristics of the external energy stimulus and internal energy signal received before collapse of each block,understanding the relationship between the time interval of successive collapse of the block and the energy received before collapse.Through the study in this paper,we not only know the dynamic mechanism of quasi-periodic events in the earthquake model,but also give theoretically the period of the system.Then we have studied the aggregation process on the geometric graph.In the fractal research,the DLA model,proposed by Witten and Sander in 1981,is a representative and influential growth model.The fractal aggregates of the DLA model have the open structure of random bifurcation.However,most fractal aggregates are irregular in nature,with a certain randomness.On the geometric graph,sites are randomly placed on the space and the connection between sites depends on the distance between them.And the network structure also has a certain randomness.Since the geometric graph is more similar to the natural system,we replaced the regular lattice in the DLA model with the geometric graph.We obtained the aggregate through numerical simulation and analyzed the effect of the randomness of the geometric graph on the structure of the aggregate.By calculating the density correlation function of the aggregate,we obtained the fractal dimension of the aggregate.The results showed that the aggregates on the geometric graph have fractal characteristics,and the fractal has an adjustable dimension.Finally,we also study the quasi-periodic properties of earthquake models on the geometric graph.Different from other earthquake models,the model not only has fixed spatial structure,but also has random connection structure.When the average degree of the network is very small,the spatial network is composed of many modules,which limits the long-distance transmission of earthquake energy.We analyze the influence of the average degree of the network on quasi-periodic events of the earthquake model,and show the dependence of the quasi-periodic events on the network size and system noise.When the average degree of the geometric graph is small,the system still has periodicity,and the period decreases with the increase of the average degree of the network.The size of the network has no influence on the periodicity.The quasi-periodic properties of the earthquake model on the geometric graph only appear when there is no noise in the system.