Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: History-dependent synchronization in the Burridge-Knopoff model   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.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org