4.7 Article

Stability of rotatory solitary states in Kuramoto networks with inertia

期刊

PHYSICAL REVIEW E
卷 105, 期 2, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.105.024203

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资金

  1. Ministry of Science and Higher Education of the Russian Federation [0729-2020-0036]
  2. Russian Science Foundation [19-12-00367]
  3. Scientific and Education Mathematical Center Mathematics for Future Technologies [075-02-2020-1483/1]
  4. National Science Foundation (USA) [DMS-1909924, CMMI-2009329]

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This study investigates the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and phase-lagged coupling. The findings show that the size of the coherent cluster and the coupling type have different effects on the stability of the solitary state.
Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and oscillates with a different frequency. Such chimera-type patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and a phase-lagged coupling. The presence of inertia can induce rotatory dynamics of the phase difference between the solitary oscillator and the coherent cluster. We derive asymptotic stability conditions for such a solitary state as a function of inertia, network size, and phase lag that may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (1) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and (2) the solitary state can be stable in small-size networks with all repulsive coupling. We also discuss the implications of our stability analysis for the emergence of rotatory chimeras.

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