Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-$\cal{PT}$ symmetry in nonlinearly damped dynamical systems and
  tailoring $\cal{PT}$ regions with position dependent loss-gain profiles   We investigate the remarkable role of position dependent damping in
determining the parametric regions of symmetry breaking in nonlinear
$\cal{PT}$-symmetric systems. We illustrate the nature of $\cal{PT}$-symmetry
preservation and breaking with reference to a remarkable integrable scalar
nonlinear system. In the two dimensional cases of such position dependent
damped systems, we unveil the existence of a class of novel
bi-$\cal{PT}$-symmetric systems which have two fold $\cal{PT}$ symmetries. We
analyze the dynamics of these systems and show how symmetry breaking occurs,
that is whether the symmetry breaking of the two $\cal{PT}$ symmetries occurs
in pair or occurs one by one. The addition of linear damping in these
nonlinearly damped systems induces competition between the two types of
damping. This competition results in a $\cal{PT}$ phase transition in which the
$\cal{PT}$ symmetry is broken for lower loss/gain strength and is restored by
increasing the loss/gain strength. We also show that by properly designing the
form of the position dependent damping, we can tailor the $\cal{PT}$-symmetric
regions of the system.

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci