Analytical study of neural networks with superdiffusive coupling supporting chimera states

The development of synchronization and chimera states plays an extremely important role in the collective activity of systems of interacting neurons. For this reason, it is crucial from both fundamental and applied perspectives to investigate empirically relevant (in a biological sense) configuration models that support analytical studies of the development of partial synchronization states. Herein we consider a system of superdiffusively coupled neurons from the limiting case perspective of the linear stability of two-component reaction-superdiffusion equations. It is found that extended linear analysis in the parameter space of the fractional Laplace operator exponents is able to characterize the configuration features of networks of superdiffusively coupled neurons supporting both the development of full and partial synchronization, as well as states of full incoherence. The possibility of not only numerical but also analytical study in a continuous perspective of superdiffusion neural networks opens new opportunities for problems of chimera state control, as well as providing extended possibilities to design functional zones on the basis of these systems.