Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Dynamics of a Class of Coupled Oscillators Driven by White
  Noises   This paper is devoted to the study of the asymptotic dynamics of a class of
coupled second order oscillators driven by white noises. It is shown that any
system of such coupled oscillators with positive damping and coupling
coefficients possesses a global random attractor. Moreover, when the damping
and the coupling coefficients are sufficiently large, the global random
attractor is a one-dimensional random horizontal curve regardless of the
strength of the noises, and the system has a rotation number, which implies
that the oscillators in the system tend to oscillate with the same frequency
eventually and therefore the so called frequency locking is successful. The
results obtained in this paper generalize many existing results on the
asymptotic dynamics for a single second order noisy oscillator to systems of
coupled second order noisy oscillators. They show that coupled damped second
order oscillators with large damping have similar asymptotic dynamics as the
limiting coupled first order oscillators as the damping goes to infinite and
also that coupled damped second order oscillators have similar asymptotic
dynamics as their proper space continuous counterparts, which are of great
practical importance.

27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys