Birth and Death of Chimera: Interplay of Delay and Multiplexing

The chimera state with co-existing coherent-incoherent dynamics has recently attracted a lot of attention due to its wide applicability. We investigate non-locally coupled identical chaotic maps with delayed interactions in the multiplex network framework and find that an interplay of delay and multiplexing brings about an enhanced or suppressed appearance of chimera state depending on the distribution as well as parity of delay values in the layers. Additionally, we report a layer chimera state with an existence of one layer displaying coherent and another layer demonstrating incoherent dynamical evolution. The rich variety of dynamical behavior demonstrated here can be used to gain further insight into the real-world networks which inherently possess such multi-layer architecture with delayed interactions. Introduction. Over the last few decades, the field of network science has witnessed tremendous growth owing to its applicability in real-world systems ranging from biology and sociology to economics [1–3]. One of the prime focus of network science is to study the collective behaviour of dynamical units coupled on these networks [4]. Coupled dynamical units are shown to exhibit a plethora of novel phenomena [5]. One such phenomenon is the emergence of chimera [6]. Initiated by the works of Kuramoto, Battogtokh and Shima [7] and later christened by Abrams and Strogatz [8], chimera state represents a hybrid dynamical state with co-existing coherence and incoherence in an identical network with symmetric coupling environment. Since then, numerous theoretical [9, 10] as well as experimental investigations [11, 12] have been reported for the observation of chimera state in various systems [6, 10, 12, 13]. Moreover, different types of chimera state have been proposed to incorporate a variety of stable and unstable co-existing coherent-incoherent state [6]. Chimera states have provided a framework to understand epileptic seizures [14,15] and unihemispheric sleep recently observed in human [16]. It has also been associated with (a)Corresponding Author (Email: [email protected]) motion of heart vessels to explain ventricular filtration [17] as well as with the so-called bump state in neural networks [18]. Furthermore, recent years have witnessed a burst of studies pertaining to the analysis of multiplex networks which is defined as a collection of two or more layers having mirror nodes in each layer [19]. An objective of multiplex network framework is to study multiple levels of interactions where function of one layer gets affected by the properties of other layers [20]. Yet another approach for understanding real world systems through network theory is to incorporate time delays. An analysis of impact of time delay on dynamical properties of a coupled system is very crucial to predict and explain dynamic evolution of such systems [21]. Numerous dynamical phenomena, including enhancement or suppression of synchronization, have been found for time delayed networks [22]. Although, it has been recently shown that chimera states exist in time delayed networks [9, 23], the occurrence of this complex spatio-temporal pattern is yet not well understood in the presence of time delay in multiplex networks.