Chimera patterns with spatial random swings between periodic attractors in a network of FitzHugh-Nagumo oscillators

For the study of symmetry-breaking phenomena in neuronal networks, simplified versions of the FitzHughNagumo model are widely used. In this paper, these phenomena are investigated in a network of FitzHugh-Nagumo oscillators taken in the form of the original model and it is found that it exhibits diverse partial synchronization patterns that are unobserved in the networks with simplified models. Apart from the classical chimera, we report a new type of chimera pattern whose incoherent clusters are characterized by spatial random swings among a few fixed periodic attractors. Another peculiar hybrid state is found that combines the features of this chimera state and a solitary state such that the main coherent cluster is interspersed with some nodes with identical solitary dynamics. In addition, oscillation death including chimera death emerges in this network. A reduced model of the network is derived to study oscillation death, which helps explaining the transition from spatial chaos to oscillation death via the chimera state with a solitary state. This study deepens our understanding of chimera patterns in neuronal networks.

Automated summary

In this paper, the study focuses on the investigation of symmetry-breaking phenomena in neuronal networks using simplified versions of the FitzHughNagumo model. The network of FitzHugh-Nagumo oscillators, in its original form, exhibits diverse partial synchronization patterns that are not observed in networks with simplified models. The study reports the discovery of a new type of chimera pattern and a peculiar hybrid state, as well as the emergence of oscillation death in the network. By deriving a reduced model, the transition from spatial chaos to oscillation death via the chimera state with a solitary state is explained. This study deepens the understanding of chimera patterns in neuronal networks.