【作者】 林敏；

【导师】 陈天仑；

【作者基本信息】 南开大学 ， 理论物理， 2005， 博士

【摘要】 本文主要研究了小世界网络中的自组织临界(SOC)行为,以及网络拓扑结构对自组织临界行为的影响。首先,基于小世界网络研究了推广的Olami-Feder-Christensen(OFC)地震模型的自组织临界行为,在这个模型中我们发现自组织临界性指纹——幂律行为,同时发现小世界网络中捷径的出现概率φ对推广的地震模型的幂律行为及其临界指数有重要影响。我们也研究了模型中的不同的连接性拓扑(“rewire”和“add”连接)对系统SOC行为的影响。然后,我们引入基于一维小世界网络具有神经生物学背景的简单神经元模型,此模型表现出自组织临界行为,并且产生长程的时间关联和1/f噪声,同时我们发现小世界网络中概率φ对模型动力学行为有重要的影响。最后,我们研究了基于小世界网络的一种脉冲耦合累积-发放神经元模型的自组织临界性和同步行为,在这个模型中发现幂律行为并且伴有大范围神经元同步行为,并且研究了网络拓扑结构对累积-发放神经元模型的动力学行为的影响。同时我们发现此模型可以产生类脑电波,分析了类脑电波的复杂行为。更多还原

【Abstract】 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.更多还原