Towards a Theory for the Formation of Chimera Patterns in Complex Networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929619676954624 |
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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 |
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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 |