Bringing up of chimera-like states in oscillator networks of mixed topologies
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Bringing up of chimera-like states in oscillator networks of mixed topologies Paramasivam Chandran 1 , Ramupillai Gopal 2 , Vallipalayam Kuppusamy Chandrasekar 2,a , and Nallamanian Athavan 1 1
2
Department of Physics, H. H. The Rajah’s College (affiliated to Bharathidasan University), Pudukkottai 622 001, Tamil Nadu, India Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India Received 30 April 2020 / Received in final form 5 August 2020 / Accepted 17 August 2020 Published online 16 September 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. In a globally coupled network of chaotically oscillating identical R¨ ossler 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 (RT h ) to trigger chimera-like states changes as we alter the coupling radius. Precisely, we see that RT h decreases as we increase the coupling radius. When we widen our scope of study to the small-world networks we find that RT h 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.
1 Introduction Chimera state, a unique dynamical state, consists of coexisting domains of coherent and incoherent oscillations basically emerges in networks of coupled systems with identical entities. During the last few decades, a number of studies have been undertaken on such emerging phenomenon makes it an active area of research [1–4]. Also, enormous works reported in the recent literature reveal that chimera-like states have been perceived as a prime exhibit in terms of both theoretical and experimental analyses on complex networks. A few to mention among their theoretical observations are in time discrete maps [5–8], chaotic models [6,9], limit cycle oscillators [10,11], neural systems [9,12], quantum mechanical oscillators [13], population dynamics [14,15], and Boolean networks [16]. More interestingly, these states have also been realized experimentally in diverse network systems belong to optics [17], electronics [17,18], opto-electronics [19], chemistry [20,21], electrochemistry [22] and mechanics [23]. One can easily rec
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