Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly coupled two slow- two fast systems, folded node and mixed mode
  oscillationsM   We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled
slow/fast oscillators. We focus on the existence and properties of a folded
singularity called FSN II that allows the emergence of MMOs in the presence of
a suitable global return mechanism. As FSN II corresponds to a transcritical
bifurcation for a desingularized reduced system, we prove that, under certain
non-degeneracy conditions, such a transcritical bifurcation exists. We then
apply this result to the case of two coupled systems of FitzHugh- Nagumo type.
This leads to a non trivial condition on the coupling that enables the
existence of MMOs.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin