Influence Of Network Topologies To Self-organized Critical Behavior

This dissertation studies the Self-organized Criticality(SOC) behavior in small world networks and the influence of network topologies to SOC behaviors. At first, we introduce a modified Olami-Feder-Christensen (OFC) earthquake model on a small world network. We find power law behavior (the fingerprint of SOC) in our new model. As the same time, we find this behavior and some basic exponents of the model depend on φ, the density of short paths in small world network. We also investigate the influence of different connectivity topologies ("rewire" and "add" connectivity) to SOC behavior. Then we introduce a simple neuron model based on the one-dimensional small world network, which has neurobiological features. Our model can display SOC behavior, and generate long-range temporal correlations and 1/f noise. More importantly, we find that effects of φ in the small world networks on the dynamical behavior of the model. At last, we investigate SOC and synchronization of a pulse-coupled integrate-and-fire neuron model based on small world networks. We find power law behavior accompanied with the large-scale synchronized activities among the units in our model, and study the influence of network topologies to the dynamical behavior. We find EEG-like signals produced by such model, and analyze their complex behavior.