Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronization, chaos, and breakdown of collective domain oscillations
  in reaction-diffusion systems   The universal equations describing collective oscillations of the multidomain
patterns of small period in an arbitrary $d$-dimensional reaction-diffusion
system of the activator-inhibitor type are asymptotically derived. It is shown
that not far from the instability leading to the formation of the pulsating
multidomain pattern the oscillations of different domains synchronize. In one
dimension standing and traveling waves of the oscillation phase are realized.
In addition to these, in two dimensions target and spiral waves of the
oscillation phase, as well as spatio-temporal chaos of domain oscillations, are
feasible. Further inside the unstable region the collective oscillations break
down, so the pulsating multidomain pattern transforms into an irregular
pulsating pattern, the uniform self-oscillations, or turbulence. The parameter
regions where these effects occur are analyzed. The effects of the pattern's
disorder are also studied. The conclusions of the analysis are supported by the
numerical simulations of a concrete model. The obtained results explain the
dynamics of Turing patterns observed in the experiments on
chlorite-iodide-malonic acid reaction.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga