History-dependent synchronization in the Burridge-Knopoff model

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dc.creatorSzkutnik, J.
dc.creatorKawecka-Magiera, B.
dc.creatorKulakowski, K.
dc.date2003-10-21
dc.date.accessioned2026-07-07T05:35:01Z
dc.date.available2026-07-07T05:35:01Z
dc.descriptionA three-blocks Burridge-Knopoff model is investigated. The dimensionless velocity-dependent friction force $F(v)\propto (1+av)^{-1}$ is linearized around $a=0$. In this way, the model is transformed into a six-dimensional mapping $\mathbf{x}(t_{n})\to \mathbf{x}(t_{n+1})$, where $t_n$ are time moments when a block starts to move or stops. Between these moments, the equations of motion are integrable. For $a<0.1$, the motion is quasiperiodic or periodic, depending on the initial conditions. For the periodic solution, we observe a synchronization of the motion of the lateral blocks. For $a>0.1$, the motion becomes chaotic. These results are true for the linearized mapping, linearized numerical and non-linearized numerical solutions.
dc.description11 pages, 12 figures, 30th Leeds-Lyon Symposium on Tribology, Sep. 2-5, 2003
dc.identifierhttps://arxiv.org/abs/nlin/0310030
dc.identifierhttp://arxiv.org/abs/nlin/0310030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80584
dc.subjectAdaptation and Self-Organizing Systems
dc.titleHistory-dependent synchronization in the Burridge-Knopoff model
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