Imperfect Amplitude Mediated Chimera States in a Nonlocally Coupled Network

We investigate the dynamical transitions in a network of nonlocally coupled Stuart-Landau oscillators with a combination of attractive and repulsive couplings. The competing interaction between the couplings plays a crucial role in many realistic situations, particularly in neuronal systems. We report that the employed attractive and repulsive couplings induce imperfect amplitude mediated chimera state which emerges as an intermediate between the oscillatory dynamics and the oscillation death state. Each oscillator in the synchronized and desynchronized groups constituting the imperfect amplitude mediated chimera drifts between both the homogeneous and inhomogeneous oscillations as a function of time. To distinguish the homogeneous and inhomogeneous oscillations, we use the finite-time average of each oscillator. The observed distinct dynamical states are further classified by finding the strength of the inhomogeneous oscillators in the corresponding dynamical states. We also find that the number of clusters in the cluster oscillation death states exponentially decays as a function of the coupling range and obeys a power law relation. Finally, we confirm the robustness of the observed amplitude mediated chimera state by introducing a Gaussian white noise in the system