Solitary states and solitary state chimera in neural networks

E Rybalova; V S Anishchenko; G I Strelkova; A Zakharova

doi:10.1063/1.5113789

Solitary states and solitary state chimera in neural networks

Chaos. 2019 Jul;29(7):071106. doi: 10.1063/1.5113789.

Authors

E Rybalova¹, V S Anishchenko¹, G I Strelkova¹, A Zakharova²

Affiliations

¹ Department of Physics, Saratov National Research State University, 83 Astrakhanskaya Street, Saratov 410012, Russia.
² Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany.

PMID: 31370403
DOI: 10.1063/1.5113789

Abstract

We investigate solitary states and solitary state chimeras in a ring of nonlocally coupled systems represented by FitzHugh-Nagumo neurons in the oscillatory regime. We perform a systematic study of solitary states in this network. In particular, we explore the phase space structure, calculate basins of attraction, analyze the region of existence of solitary states in the system's parameter space, and investigate how the number of solitary nodes in the network depends on the coupling parameters. We report for the first time the occurrence of solitary state chimera in networks of coupled time-continuous neural systems. Our results disclose distinctive features characteristic of solitary states in the FitzHugh-Nagumo model, such as the flat mean phase velocity profile. On the other hand, we show that the mechanism of solitary states' formation in the FitzHugh-Nagumo model similar to chaotic maps and the Kuramoto model with inertia is related to the appearance of bistability in the system for certain values of coupling parameters. This indicates a general, probably a universal desynchronization scenario via solitary states in networks of very different nature.