  We report an interesting symmetry-breaking transition in coupled identical
oscillators, namely the continuous transition from homogeneous to inhomogeneous
limit cycle oscillations. The observed transition is the oscillatory analog of
the Turing-type symmetry-breaking transition from amplitude death (i.e., stable
homogeneous steady state) to oscillation death (i.e., stable inhomogeneous
steady state). This novel transition occurs in the parametric zone of
occurrence of rhythmogenesis and oscillation death as a consequence of the
presence of local filtering in the coupling path. We consider paradigmatic
oscillators, such as Stuart-Landau and van der Pol oscillators under mean-field
coupling with low-pass or all-pass filtered self-feedback and through a
rigorous bifurcation analysis we explore the genesis of this transition.
Further, we experimentally demonstrate the observed transition, which
establishes its robustness in the presence of parameter fluctuations and noise.
