There has been much interest in studying quasi-periodic events on earthquake models.Here we investigate quasiperiodic 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-word 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.