Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Common and different features between the behavior of the chaotic
  dynamical systems and the 1/f^alpha(f) noise   The major goal of the present paper is to find out the manifestation of the
boundedness of fluctuations. Two different subjects are considered: (i) an
ergodic Markovian process associated with a new type of large scaled
fluctuations at spatially homogeneous reaction systems; (ii) simulated
dynamical systems that posses strange attractors. Their common property is that
the fluctuations are bounded. It is found out that the mathematical description
of the stochasity at both types of systems is identical. Then, it is to be
expected that it exhibits certain common features whose onset is the
stochasticity, namely: (i) The power spectrum of a time series of length $T$
comprises a strictly decreasing band that uniformly fits the shape
$1/f^\alpha(f)$ where $\alpha(1/T)=1$ and $\alpha(f)$ strictly increases to the
value $\alpha(\inf)=p$ ($p>2$) as $f$ approaches infinity. Practically, at low
frequencies this shape is $1/f$-like with high accuracy because the deviations
of the non-constant exponent $\alpha(f)$ from 1 are very small and become even
smaller as the frequency tends to 1/T. The greatest advantage of the shape
$1/\alpha(f)$ is that it ensures a finite variance of the fluctuations. (ii) It
is found out that the structure of a physical and strange attractor is
identical and they are non-homogeneous. (iii) The Kolmogorov entropy is finite.

27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess