Emergence of chimera in multiplex network

Abstract

Chimera is a relatively new emerging phenomenon where coexistence of synchronous and asynchronous states is observed in symmetrically coupled dynamical units. We report the observation of the chimera state in multiplex networks where individual layer is represented by 1-d lattice with nonlocal interactions. While, multiplexing does not change the type of the chimera state and retains the multi-chimera state displayed by the isolated networks, it changes the regions of the incoherence. We investigate the emergence of coherent-incoherent bifurcation upon varying the control parameters, namely, the coupling strength and the network size. Additionally, we investigate the effect of initial condition on the dynamics of the chimera state. Using a measure based on the differences between the neighboring nodes which distinguishes smooth and nonsmooth spatial profiles, we find the critical coupling strength for the transition to the chimera state. Observing chimera in a multiplex network with one-to-one inter layer coupling is important to gain insight to many real world complex systems which inherently posses multilayer architecture. © 2016 World Scientific Publishing Company.