  A 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.
