  We report a transition from homogeneous steady state to inhomogeneous steady
state in coupled oscillators, both limit cycle and chaotic, under cyclic
coupling and diffusive coupling as well when an asymmetry is introduced in
terms of a negative parameter mismatch. Such a transition appears in limit
cycle systems via pitchfork bifurcation as usual. Especially, when we focus on
chaotic systems, the transition follows a transcritical bifurcation for cyclic
coupling while it is a pitchfork bifurcation for the conventional diffusive
coupling. We use the paradigmatic Van der Pol oscillator as the limit cycle
system and a Sprott system as a chaotic system. We verified our results
analytically for cyclic coupling and numerically check all results including
diffusive coupling for both the limit cycle and chaotic systems.
