Amplitude Mediated Chimera States with Active and Inactive Oscillators

Abstract: The emergence and nature of amplitude mediated chimera states, spatio-temporal patterns of co-existing coherent and incoherent regions, are investigated for a globally coupled system of active and inactive Ginzburg-Landau oscillators. The existence domain of such states is found to shrink and shift in parametric space as the fraction of inactive oscillators is increased. The role of inactive oscillators is found to be two fold - they get activated to form a separate region of coherent oscillations and in addition decrease the common collective frequency of the coherent regions by their presence. The dynamical origin of these effects is delineated through a detailed bifurcation analysis of a reduced model equation that is based on a mean field approximation. Our results may have practical implications for the robustness of such states in biological or physical systems where age related deterioration in the functionality of components can occur.