Bringing up of chimera-like states in oscillator networks of mixed topologies

Abstract

In a globally coupled network of chaotically oscillating identical Rossler systems, chimera-like states have been made to exist by strengthening, appropriate links of a node that fall under nonlocal topology with additional weak signals, sequentially to sufficient number of nodes of the network. We find a power-law dependence of the distance of oscillators with the spatial correlation function which reveals that the obtained chimera-like states belong to phase chimera category. Further, we define a quantity R to denote the ratio of nodes with additional weak nonlocal strength and observe that the threshold value of it (RTh) to trigger chimera-like states changes as we alter the coupling radius. Precisely, we see that RTh decreases as we increase the coupling radius. When we widen our scope of study to the small-world networks we find that RTh decreases for higher probability values. In addition, we have shown that the chimera-like states even exist when we restrict the additional weak nonlocal signals to be one-sided. We determine the nature of different dynamical states by using the values of strength of incoherence, in general, and category of chimera-like states by means of spatial correlation function, in particular.