Chimera states in a lattice of superdiffusively coupled neurons

Abstract

Chimera states are a truly remarkable dynamical phenomenon that occur in systems of coupled oscillators. In this regime, regions of synchronized and unsynchronized elements are formed in the system. For many applied problems, especially in neuroscience, these states offer a rich potential for research. However, the plethora of models and the lack of a ”single simple principle” that leads to the development of chimeras makes it very difficult to understand their nature. In this work, we propose a three-component reaction-superdiffusion system based on a unified mechanism founded on the properties of the fractional Laplace operator and the nonlinear Hindmarsh-Rose model functions. In the proposed system, the non-local type of interaction forming the coupling between the elements depends significantly on the fractional Laplace operator exponents of the corresponding components. It is shown that in the framework of the superdiffusion type of interaction, chimera states are realized in the system. At the same time, many qualitative (shape, visual degree of inhomogeneity and area size) and quantitative characteristics of chimeras (synchronization factor, strength of incoherence, local order parameter, number of elements with a potential value exceeding a given one) depend significantly on the exponents of the fractional Laplace operator. In addition to classical chimeras and target-waves chimeras, the results of numerical simulations show the presence of mutually sustaining reaction processes of different scales in the system.