Trade-off between filtering and symmetry breaking mean-field coupling in inducing macroscopic dynamical states

Abstract

We study the manifestation of the competing interaction between the mean-field intensity and the symmetry breaking coupling on the phenomenon of aging transition in an ensemble of limit-cycle oscillators comprising of active and inactive oscillators. Further, we also introduce filtering in both the intrinsic and extrinsic variables of the mean-field diffusive coupling to investigate the counter-intuitive effect of both filterings. We find that large values of the mean-field intensity near unity favor the oscillatory nature of the ensemble, whereas low values favor the onset of the aging transition and heterogeneous dynamical states such as cluster oscillation death and chimera death states even at low values of the symmetry breaking coupling strength. Heterogeneous dynamical states predominates at large values of the coupling strength in all available parameter spaces. We also uncover that even a weak intrinsic filtering favors the aging transition and heterogeneous dynamical states, while a feeble extrinsic filtering favors the oscillatory state. Chimera death state is observed among the active oscillators for the first time in the aging literature. Our results can lead to engineering the dynamical states as desired by an appropriate choice of the control parameters. Further, the transition from the oscillatory to the aging state occurs via an inverse Hopf bifurcation, while the transition from the aging state to the cluster oscillation death states emerges through a supercritical pitch-fork bifurcation. The deduced analytical bifurcation curves are in good agreement with the numerical boundaries of the observed dynamical states. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.