The present paper is the second part of a brief survey of development of the Kuramoto model of coupled phase oscillators. We consider several systems obtained as generalizations of the classical Kuramoto model and given on symmetric oscillatory networks for different functions of interaction between elements. We describe the collective dynamics and bifurcations of transitions between different regimes of interacting elements, namely, full and partial synchronizations, global antiphase regime, and slow switching. We reveal the relationship between the symmetries of the network and the existence of invariant manifolds of the system, cluster states, and more complicated collective regimes. We also describe dynamics of the model with central element and the systems with circulant and modular networks. The coexistence of conservative and dissipative dynamics, as well as the existence of chimera states and the competition for synchronization regimes are demonstrated.
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Translated from Neliniini Kolyvannya, Vol. 22, No. 3, pp. 312–340, July–September, 2019.
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Burylko, O.A. Collective Dynamics and Bifurcations in Symmetric Networks of Phase Oscillators. II. J Math Sci 253, 204–229 (2021). https://doi.org/10.1007/s10958-021-05223-7
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DOI: https://doi.org/10.1007/s10958-021-05223-7