Towards a Theory for the Formation of Chimera Patterns in Complex Networks

Fuente: arXiv
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Main Authors: Asllani, Malbor, Arenas, Alex
Format: Preprint
Published: 2024
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author Asllani, Malbor
Arenas, Alex
author_facet Asllani, Malbor
Arenas, Alex
contents Chimera states, marked by the coexistence of order and disorder in systems of coupled oscillators, have captivated researchers with their existence and intricate patterns. Despite ongoing advances, a fully understanding of the genesis of chimera states remains challenging. This work formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks, in a similar way to how Turing patterns are produced. Employing linear stability analysis and the spectral properties of complex networks, we show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. Our findings suggest that chimeras result from the interplay between local and global dynamics at different time scales. Validated through simulations and empirical network analyses, our method enriches the understanding of coupled oscillator dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2412_05504
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Towards a Theory for the Formation of Chimera Patterns in Complex Networks
Asllani, Malbor
Arenas, Alex
Adaptation and Self-Organizing Systems
Pattern Formation and Solitons
Chimera states, marked by the coexistence of order and disorder in systems of coupled oscillators, have captivated researchers with their existence and intricate patterns. Despite ongoing advances, a fully understanding of the genesis of chimera states remains challenging. This work formalizes a systematic method by evoking pattern formation theory to explain the emergence of chimera states in complex networks, in a similar way to how Turing patterns are produced. Employing linear stability analysis and the spectral properties of complex networks, we show that the randomness of network topology, as reflected in the localization of the graph Laplacian eigenvectors, determines the emergence of chimera patterns, underscoring the critical role of network structure. In particular, this approach explains how amplitude and phase chimeras arise separately and explores whether phase chimeras can be chaotic or not. Our findings suggest that chimeras result from the interplay between local and global dynamics at different time scales. Validated through simulations and empirical network analyses, our method enriches the understanding of coupled oscillator dynamics.
title Towards a Theory for the Formation of Chimera Patterns in Complex Networks
topic Adaptation and Self-Organizing Systems
Pattern Formation and Solitons
url https://arxiv.org/abs/2412.05504