Traveling chimera patterns in a two-dimensional neuronal network

We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, i.e. the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of the instantaneous local order parameter in two dimensions. Finally weextend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of patterns' propagationin two dimensions. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Our study focuses on the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the presence of both local and non-local couplings. We found that the unique presence of non-linear chemical coupling can lead to the traveling chimera phenomenon, while the interaction of local electrical coupling and non-local coupling can generate various phenomena like traveling chimera and alternating patterns. The confirmation of coherence states is done through the introduction of the parameter of the instantaneous local order parameter in two dimensions, and the direction of patterns' propagation in two dimensions is determined using mathematical tools such as the Hamilton energy function.