  The competing effect of heterogeneity and symmetry breaking coupling on the
emerging dynamics in a system of N globally coupled Stuart-Landau oscillators
is investigated. Increasing the heterogeneity, using the standard deviation of
the Hopf bifurcation parameter, favors the macroscopic oscillatory state for
low values of the symmetry breaking coupling and inhomogeneous steady state for
larger values of the coupling. There is also a transition, tipping, to
homogeneous steady state (aging state) from the macroscopic oscillatory state.
The limiting factor in the diffusive coupling favors the macroscopic
oscillatory state even in the presence of a large fraction of inactive
oscillators in the network thereby increasing the robustness of the network.
The globally coupled oscillators are reduced to a system of two evolution
equations for the macroscopic order parameters, corresponding to the mean-field
and the shape parameter, using the self-consistent field approach. The
bifurcation diagrams obtained from the mean-field variables elucidate various
bifurcation scenarios responsible for the dynamical transitions observed in N
globally coupled Stuart-Landau oscillators. In particular, tipping to the aging
state is found to occur via the Hopf and pitchfork bifurcations illustrating
the phenomenon of bifurcation induced tipping. Analytical stability (critical)
curves of these bifurcations, deduced from the mean-field variables, are found
to fairly well agree with the simulation results.
