Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new approach to fuzzy sets: Application to the design of nonlinear
  time-series, symmetry-breaking patterns, and non-sinusoidal limit-cycle
  oscillations   It is shown that characteristic functions of sets can be made fuzzy by means
of the $\mathcal{B}_{\kappa}$-function, recently introduced by the author,
where the fuzziness parameter $\kappa \in \mathbb{R}$ controls how much a fuzzy
set deviates from the crisp set obtained in the limit $\kappa \to 0$. As
applications, we present first a general expression for a switching function
that may be of interest in electrical engineering and in the design of
nonlinear time-series. We then introduce another general expression that allows
wallpaper and frieze patterns for every possible planar symmetry group (besides
patterns typical of quasicrystals) to be designed. We show how the fuzziness
parameter $\kappa$ plays an analogous role to temperature in physical
applications and may be used to break the symmetry of spatial patterns. As a
further, important application, we establish a theorem on the shaping of limit
cycle oscillations far from bifurcations in smooth deterministic nonlinear
dynamical systems governed by differential equations. Following this
application, we briefly discuss a generalization of the Stuart-Landau equation
to non-sinusoidal oscillators obtained as a consequence of our theorem.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th