Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for
  coupled oscillators on simplicial complexes   We formulate a general Kuramoto model on weighted simplicial complexes where
phases oscillators are supported on simplices of any order $k$. Crucially, we
introduce linear and non-linear frustration terms that are independent of the
orientation of the $k+1$ simplices, providing a natural generalization of the
Sakaguchi-Kuramoto model. In turn, this provides a generalized formulation of
the Kuramoto higher-order parameter as a potential function to write the
dynamics as a gradient flow. We study the properties of the dynamics of the
simplicial Sakaguchi-Kuramoto model with oscillators on edges using a selection
of simplicial complexes of increasingly complex structure, to highlight the
complexity of dynamical behaviors emerging from even simple simplicial
complexes. In particular, using the Hodge decomposition of the solution, we
understand how the nonlinear frustration couples the dynamics in orthogonal
subspaces. We discover various dynamical phenomena, such as the partial loss of
synchronization in subspaces aligned with the Hodge subspaces and the emergence
of simplicial phase re-locking in regimes of high frustration.

5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin