Regular Article

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

¹ Department of Physics, H. H. The Rajah’s College (affiliated to Bharathidasan University), Pudukkottai 622 001, Tamil Nadu, India
² Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India

^a e-mail: chandru25nld@gmail.com

Received: 30 April 2020
Received in final form: 5 August 2020
Accepted: 17 August 2020
Published online: 16 September 2020

Abstract

In a globally coupled network of chaotically oscillating identical Rössler 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 (R_Th) to trigger chimera-like states changes as we alter the coupling radius. Precisely, we see that R_Th decreases as we increase the coupling radius. When we widen our scope of study to the small-world networks we find that R_Th 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.