Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern selection in the Schnakenberg equations: From normal to
  anomalous diffusion   Pattern formation in the classical and fractional Schnakenberg equations is
studied to understand the nonlocal effects of anomalous diffusion. Starting
with linear stability analysis, we find that if the activator and inhibitor
have the same diffusion power, the Turing instability space depends only on the
ratio of diffusion coefficients $\kappa_1/\kappa_2$. However, the smaller
diffusive powers might introduce larger unstable wave numbers with wider band,
implying that the patterns may be more chaotic in the fractional cases. We then
apply a weakly nonlinear analysis to predict the parameter regimes for spot,
stripe, and mixed patterns in the Turing space. Our numerical simulations
confirm the analytical results and demonstrate the differences of normal and
anomalous diffusion on pattern formation. We find that in the presence of
superdiffusion the patterns exhibit multiscale structures. The smaller the
diffusion powers, the larger the unstable wave numbers and the smaller the
pattern scales.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat