Spatiotemporal structures in an ensemble of nonlocally coupled Nekorkin maps

Background and Objectives: Studying chimera states is a subject of special attention among specialists in nonlinear dynamics, and the issue on the mechanisms for implementing chimeras is today one of the topic directions. In the paper we consider the mechanism for realizing a chimera state regime which is based on the so-called “solitary states” (SSC) and is actively discussed by experts. The problem is solved by analyzing the dynamics of a one-dimensional ring of nonlocally coupled discrete-time systems. The individual element of the ring is given by the discrete model describing neuronal activity. Materials and Methods: Numerical simulation of large and multicomponent ensembles (networks) is the basic method of our research. Software systems specially developed by the authors are used that allow to carry out numerical experiments under variations in the system parameters, initial conditions and provide a graphic illustration of the obtained results. Results: We have established that the ensemble of nonlocally coupled Nekorkin maps can exhibit the SSC regime which is resulted from the appearance of bistability in the individual elements of the ensemble. This fact has been corroborated by the numerical results for the phase portraits of the coexisting attractors and their basins of attraction. It has been shown that randomly distributed initial conditions lead to the situation when one part of the ensemble oscillators fall into one attractor, while the other one belongs to the second attracting set. This mechanism was presented by the authors in the previously published papers for ensembles of different discrete-time systems. The results of this work confirm the commonality of the mechanism for implementing the SSC mode established earlier by the authors. Conclusion: The results of this article make a significant contribution to the understanding of the peculiarities in the formation of complex spatiotemporal structures of the SSC type.