Abstract There has been much interest in studying quasi-periodic events on earthquake models. Here we investigate quasi-periodic events in the avalanche time series on structured earthquake models by the analysis of the autocorrelation function and the fast Fourier transform. For random spatial earthquake models, quasi-periodic events are robust and we obtain a simple rule for a period that is proportional to the choice of unit time and the dissipation of the system. Moreover, computer simulations validate this rule for two-dimensional lattice models and cycle graphs, but our simulation results also show that small-world models, scale-free models, and random rule graphs do not have periodic phenomena. Although the periodicity of avalanche does not depend on the criticality of the system or the average degree of the system or the size of the system, there is evidence that it depends on the time series of the average force of the system.

中文翻译：

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结构化地震模型上的准周期事件*

摘要 在地震模型上研究准周期事件引起了人们的极大兴趣。在这里，我们通过分析自相关函数和快速傅里叶变换来研究结构化地震模型上雪崩时间序列中的准周期事件。对于随机空间地震模型，准周期事件是稳健的，我们获得了一个简单的周期规则，该规则与单位时间的选择和系统的耗散成正比。此外，计算机模拟验证了二维晶格模型和循环图的这一规则，但我们的模拟结果也表明，小世界模型、无标度模型和随机规则图不存在周期性现象。