ar X iv : n lin / 0 31 00 30 v 1 [ nl in . A O ] 2 1 O ct 2 00 3 History - dependent synchronization in the Burridge - Knopoff model
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چکیده
A three-blocks Burridge-Knopoff model is investigated. The dimension-less velocity-dependent friction force F (v) ∝ (1 + av) −1 is linearized around a = 0. In this way, the model is transformed into a six-dimensional mapping x(t n) → 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.
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تاریخ انتشار 2008