We discuss the occurrence of different kinds of chimera states such as transient amplitude chimera, stable amplitude chimera and imperfect breathing chimera states in a locally coupled network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibit oscillations with large amplitudes while the desynchronized group of oscillators oscillate with small amplitudes and this behavior of coexistence of synchronized and desynchronized oscillations fluctuate with time. The existence of imperfect breathing chimera state is confirmed through the localized set approach and by finding the relative phases of the oscillators. The choice of cluster initial condition has been found to support the presence of the above mentioned dynamical states including amplitude chimera state and imperfectly breathing chimera state. Then we have analyzed the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyzed the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We have also found that the transient time of the amplitude chimera state increases if the system of oscillators are coupled through nonlocal interaction.
