Effect of hidden geometry and higher-order interactions on the synchronization and hysteresis behaviour of phase oscillators on 5-cliques simplicial assemblies
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914380251136000 |
|---|---|
| author | Sahoo, Samir Tadic, Bosiljka Chutani, Malayaja Gupte, Neelima |
| author_facet | Sahoo, Samir Tadic, Bosiljka Chutani, Malayaja Gupte, Neelima |
| contents | The hidden geometry of simplicial complexes can influence the collective dynamics of nodes in different ways depending on the simplex-based interactions of various orders and competition between local and global structural features. We study a system of phase oscillators attached to nodes of 4-dimensional simplicial complexes and interacting via positive/negative edges-based pairwise $K_1$ and triangle-based triple $K_2\geq 0$ couplings. Three prototypal simplicial complexes are grown by aggregation of 5-cliques, controlled by the chemical affinity parameter $ν$, resulting in sparse, mixed, and compact architecture, all of which have 1-hyperbolic graphs but different spectral dimensions. By changing the interaction strength $K_1\in[-4,2]$ along the forward and backward sweeps, we numerically determine individual phases of each oscillator and a global order parameter to measure the level of synchronisation. Our results reveal how different architectures of simplicial complexes, in conjunction with the interactions and internal-frequency distributions, impact the shape of the hysteresis loop and lead to patterns of locally synchronised groups that hinder global network synchronisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14894 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effect of hidden geometry and higher-order interactions on the synchronization and hysteresis behaviour of phase oscillators on 5-cliques simplicial assemblies Sahoo, Samir Tadic, Bosiljka Chutani, Malayaja Gupte, Neelima Statistical Mechanics Adaptation and Self-Organizing Systems The hidden geometry of simplicial complexes can influence the collective dynamics of nodes in different ways depending on the simplex-based interactions of various orders and competition between local and global structural features. We study a system of phase oscillators attached to nodes of 4-dimensional simplicial complexes and interacting via positive/negative edges-based pairwise $K_1$ and triangle-based triple $K_2\geq 0$ couplings. Three prototypal simplicial complexes are grown by aggregation of 5-cliques, controlled by the chemical affinity parameter $ν$, resulting in sparse, mixed, and compact architecture, all of which have 1-hyperbolic graphs but different spectral dimensions. By changing the interaction strength $K_1\in[-4,2]$ along the forward and backward sweeps, we numerically determine individual phases of each oscillator and a global order parameter to measure the level of synchronisation. Our results reveal how different architectures of simplicial complexes, in conjunction with the interactions and internal-frequency distributions, impact the shape of the hysteresis loop and lead to patterns of locally synchronised groups that hinder global network synchronisation. |
| title | Effect of hidden geometry and higher-order interactions on the synchronization and hysteresis behaviour of phase oscillators on 5-cliques simplicial assemblies |
| topic | Statistical Mechanics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2305.14894 |