Chimera states in systems of superdiffusively coupled neurons

Abstract

Background and Objectives: One of the most intriguing collective phenomena, which arise in systems of coupled oscillators of different nature, are chimera states. They are characterized by the emergence of coordinated spatial synchronization and desynchronization, in an initially homogeneous system. Materials and Methods: This paper discusses the results of studies of one-dimensional and two-dimensional systems of interacting neurons organized on the basis of the fractional Laplace operator and the superdiffusion kinetic mechanism. Their use significantly extends the possibilities of describing chimera-like phenomena from the position of the classical reaction-diffusion approach. Due to mathematical brevity and its ability to reproduce almost all known scenarios of point neural activity, Hindmarsh–Rose model functions were used as a nonlinear part. Results: The studies under discussion demonstrate that one-dimensional and two-dimensional systems, two and three-component reaction-superdiffusion equations organized on the basis the fractional Laplace operator are able to reproduce chimera states. Dynamic regimes in the parameter space of the fractional Laplace operator exponents associated with the shape-forming features of networks of interacting neurons have been analyzed. Parameter regions of synchronization modes, modes of incoherent behavior, and chimera states are discussed. Conclusion: The results of the presented studies can be used in computational neuroscience tasks and various interdisciplinary studies as an alternative to existing network models.

Keywords

• chimera states
• superdiffusion
• fractional laplace operator
• systems of interacting neurons
• complex systems