# gst: emergence of the traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera in a two-dimensional network

<< Neuronal synchronization being a phenomenon linked to several brain pathologies such as epilepsy, Parkinson diseases, Alzheimer, autism and schizophrenia, does not always appear in a singular way in neuronal networks. Its presence (state of coherence) accompanied simultaneously by an asynchronous state (state of incoherence) has been demonstrated (..) in the networks of identical oscillators not locally coupled. This phenomenon was later termed the chimera state. (..) Chimera states are analogously to the cerebral behaviors of certain aquatic mammals and migratory birds, which during their movements half part of their brains asleep while the rest are awake.  >>️

AA << study the emergence of the traveling chimera state in a two-dimensional network of (..) burst neurons with the mutual presence of local and non-local couplings. (AA) 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, ie 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 instantaneous local order parameter in two dimensions. >>️

Gael R. Simo, Patrick Louodop, et al. Traveling chimera patterns in two-dimensional neuronal network. arXiv:2106.08400v1. Jun 9, 2021.

https://arxiv.org/abs/2106.08400