Traveling chimera patterns in two-dimensional neuronal network

TL;DR

This paper investigates the emergence and dynamics of traveling chimera patterns in a two-dimensional neuronal network with mixed local and non-local couplings, revealing complex movement behaviors and their underlying mechanisms.

Contribution

It introduces a novel analysis of traveling chimera states in 2D neuronal networks with combined couplings, including mathematical tools to determine pattern propagation directions.

Findings

Traveling chimera patterns occur with non-local chemical coupling.

Mixed local and non-local couplings generate diverse traveling patterns.

Mathematical analysis reveals the direction of pattern propagation.

Abstract

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, 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. We extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of propagation of patterns in two dimensions.