Local and global chimera states in a four-oscillator system.

Abstract

Emergence of distinct collective dynamical states in the two smallest populations of nonlinear oscillators with global coupling among them is delineated. In particular, considering four oscillators constituting two populations of two oscillators each, we show the emergence of local chimera, global chimera, and global amplitude chimera states by breaking the permutation symmetry within the populations, in addition to the local synchronized and global synchronized states. Further, the symmetry breaking facilitates the onset of local chimera accompanied by the anomalous synchronization even with an identical nonisochronicity parameter in contrast to the existing literature. Furthermore, the spread of local synchronized and local chimera states is found to increase upon increasing the frequency difference among the populations, while the spread of local chimera, global chimera, and global amplitude chimera states increases for larger values of the nonisochronicity parameter. In addition, we have also deduced the stability condition for the global synchronized state using both the amplitude and its phase model, and find that the global synchronized state attains stability even for smaller values of the coupling strength for the amplitude model when compared to its phase reduced model.