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We report a transition from a homogeneous steady state (HSS) to inhomogeneoussteady states (IHSSs) in a network of globally coupled identical oscillators.We perturb a synchronized population in the network with a few local negativemean field links. It is observed that the whole population splits into twoclusters for a certain number of negative mean field links and specific rangeof coupling strength. For further increases of the strength of interactionthese clusters collapse to a HSS followed by a transition to IHSSs. Weanalytically determine the origin of HSS and its transition to IHSS in relationto the number of negative mean-field links and the strength of interactionusing a reductionism approach to the model network in a two-cluster state. Weverify the results with numerical examples of networks using the paradigmaticLandau-Stuart limit cycle system and the chaotic Rossler oscillator asdynamical nodes. During the transition from HSS to IHSSs, the network followsthe Turing type symmetry breaking pitchfork or transcritical bifurcationdepending upon the system dynamics.

Transition from amplitude to oscillation death in a network of oscillators