Symmetry Analysis of Coupled Scalar Systems under Time Delay
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911208699854848 |
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| author | Atay, Fatihcan M. Ruan, Haibo |
| author_facet | Atay, Fatihcan M. Ruan, Haibo |
| contents | We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based on the equivariant degree method and its computational packages, we perform a symmetry classification of destabilizing bifurcations in bidirectional rings of coupled units. Both stationary and oscillatory bifurcations are discussed. We also introduce the concept of secondary dominating orbit types to capture bifurcating solutions of submaximal nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry Analysis of Coupled Scalar Systems under Time Delay Atay, Fatihcan M. Ruan, Haibo Pattern Formation and Solitons Dynamical Systems Adaptation and Self-Organizing Systems 34C14, 34C23, 34C15, 47H11, 34C25 We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based on the equivariant degree method and its computational packages, we perform a symmetry classification of destabilizing bifurcations in bidirectional rings of coupled units. Both stationary and oscillatory bifurcations are discussed. We also introduce the concept of secondary dominating orbit types to capture bifurcating solutions of submaximal nature. |
| title | Symmetry Analysis of Coupled Scalar Systems under Time Delay |
| topic | Pattern Formation and Solitons Dynamical Systems Adaptation and Self-Organizing Systems 34C14, 34C23, 34C15, 47H11, 34C25 |
| url | https://arxiv.org/abs/2510.11911 |