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Symmetry breaker governs synchrony patterns in neuronal inspired networks

Published 24 Mar 2024 in math.DS, nlin.CD, and nlin.PS | (2403.16261v1)

Abstract: Experiments in the human brain reveal switching between different activity patterns and functional network organization over time. Recently, multilayer modeling has been employed across multiple neurobiological levels (from spiking networks to brain regions) to unveil novel insights into the emergence and time evolution of synchrony patterns. We consider two layers with the top layer directly coupled to the bottom layer. When isolated, the bottom layer would remain in a specific stable pattern. However, in the presence of the top layer, the network exhibits spatiotemporal switching. The top layer in combination with the inter-layer coupling acts as a symmetry breaker, governing the bottom layer and restricting the number of allowed symmetry-induced patterns. This structure allows us to demonstrate the existence and stability of pattern states on the bottom layer, but most remarkably, it enables a simple mechanism for switching between patterns based on the unique symmetry-breaking role of the governing layer. We demonstrate that the symmetry breaker prevents complete synchronization in the bottom layer, a situation that would not be desirable in a normal functioning brain. We illustrate our findings using two layers of Hindmarsh-Rose (HR) oscillators, employing the Master Stability function approach in small networks to investigate the switching between patterns.

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