Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smallest chimeras under repulsive interactions   We present an exemplary system of three identical oscillators in a ring
interacting repulsively to show up chimera patterns. The dynamics of individual
oscillators is governed by the superconducting Josephson junction.
Surprisingly, the repulsive interactions establish a symmetry of compelete
synchrony in the ring, which is broken with increasing interactions when the
junctions pass through serials of asynchronous states (periodic and chaotic),
but finally emerge into chimera states. The chimera pattern appears in chaotic
rotational motion of the three junctions when two junctions evolve coherently
while the third junction is incoherent. For larger repulsive coupling, the
junctions evolves into another chimera pattern in a periodic state when two
junctions remain coherent in rotational motion and one transits to incoherent
librational motion. This chimera pattern is sensitive to initial conditions, in
the sense, that the chimera state flips to another pattern when two junctions
switch to coherent librational motion and the third junction remains in
rotational motion, but incoherent. The chimera patterns are detected by using
partial and global error functions of the junctions while the librational and
rotational motions are identified by a libration index. All the collective
states, complete synchrony, desynchronization and two chimera patterns, are
delineated in a parameter plane of the ring of junctions, where the boundaries
of complete synchrony are demarcated by using the master stability function.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg