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• W2315804914 abstract "The concept of bounded confidence in social dynamics is introduced into the Kuramoto model. Then a model with projective symmetry is naturally induced by a principal ${Z}_{2}$ bundle over a circle. A Mobius strip is constructed as the manifold of interactions such that two ``sides'' of a local section correspond to antipodal couplings with opposite signs. We show analytically that symmetric polarization of synchronized states (conformist vs contrarian) can emerge from the collective behavior of homogeneously coupled oscillators. In the continuum limit, a generalized asymmetric model reverts to the symmetric case under uniform initial condition, whereas for networks of finite size, it exhibits richer dynamics or the ordinary behavior of the classic model via symmetry breaking, depending on the relevant parameters values. The symmetry and symmetry breaking of the synchronization state are analogous to the concepts of equality and majority of opinions in sociophysical models of opinion formation. The synchronized clusters can be one (consensus), two (polarization), or more (fragmentation), as opinion clusters." @default.
• W2315804914 created "2016-06-24" @default.
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• W2315804914 date "2013-02-19" @default.
• W2315804914 modified "2023-09-27" @default.
• W2315804914 title "Symmetry and symmetry breaking in a Kuramoto model induced on a Möbius strip" @default.
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• W2315804914 doi "https://doi.org/10.1103/physreve.87.022811" @default.
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