Diverse phase transitions in Kuramoto model with adaptive mean-field coupling breaking the rotational symmetry

M. Manoranjani, D.V. Senthilkumar and V.K. Chandrasekar

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

Abstract: We consider the paradigmatic Kuramoto oscillators coupled via an adaptive mean-field variable that breaks the rotational symmetry. The evolution equation for the mean-field variable is governed by the linear ordinary differential equation corresponding to a low-pass filter with a time-scale parameter, which attenuates the mean-field signal by filtering its high frequency components. We find distinct phase transitions among the incoherent state, standing wave state and synchronized stationary state in both forward and reverse traces in the entire range of the time-scale parameter. In particular, one can observe two distinct continuous transitions, a continuous transition followed by a discontinuous transition, or a single discontinuous transition among the distinct dynamical states in the forward trace depending on the range of the time-scale parameter, which determines the degree of attenuation. Further, one can also observe two distinct continuous transitions or a single discontinuous desynchronization transition in the reverse trace depending on the time-scale parameter. We derive the evolution equations for the macroscopic order parameters governing the dynamics of the discrete set of coupled phase oscillators. We also deduce the analytical conditions for the stability of the Hopf, pitchfork and saddle–node bifurcations, and find them to be in consistent with the dynamical transitions observed using the simulation.

Keywords: Kuramoto model; Low pass filter; Symmetry breaking coupling; Explosive synchronization (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008822

DOI: 10.1016/j.chaos.2023.113981

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