  Study of collective phenomenon in populations of coupled oscillators are a
subject of intense exploration in physical, biological, neuronal and social
systems. Here we propose a scheme for the creation of chimera states, namely
the coexistence of distinct dynamical behaviors in an ensemble of multivariable
coupled oscillatory systems and a novel scheme to study their stability. We
target bifurcation parameters that can be tuned such that out of the two
coupling parameters one pushes the system to synchrony while the other one
takes it to the desynchronized state. The competition between these states
result in a situation that a certain fraction of oscillators are synchronized
while others are desynchronized thereby producing a mixed chimera state.
Further changes in couplings can result in the desired form of the state which
could be completely synchronized or desynchronized. Using the model example of
coupled R\"ossler systems we show that their basin of attraction are either
riddled or intertwined. We use Strength of incoherence and Master Stability
function (MSF) as the order parameters to verify the stability of chimera
states. MSF for different attractors are found to possess both negative and
positive values indicating the coexistence of stable synchronized dynamics with
desynchronized state.
