Properties of Quasi-synchronization Time of High-dimensional Hegselmann-Krause Dynamics
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918090142384128 |
|---|---|
| author | Su, Wei Jiang, Meiru Yu, Yongguang Chen, Ge |
| author_facet | Su, Wei Jiang, Meiru Yu, Yongguang Chen, Ge |
| contents | The behavior of one-dimensional Hegselmann-Krause (HK) dynamics driven by noise has been extensively studied. Previous research has indicated that within no matter the bounded or the unbounded space of one dimension, the HK dynamics attain quasi-synchronization (synchronization in noisy case) in finite time. However, it remains unclear whether this phenomenon holds in high-dimensional space. This paper investigates the random time for quasi-synchronization of multi-dimensional HK model and reveals that the boundedness and dimensions of the space determine different outcomes. To be specific, if the space is bounded, quasi-synchronization can be attained almost surely for all dimensions within a finite time, whereas in unbounded space, quasi-synchronization can only be achieved in low-dimensional cases (one and two). Furthermore, different integrability of the random time of various cases is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties of Quasi-synchronization Time of High-dimensional Hegselmann-Krause Dynamics Su, Wei Jiang, Meiru Yu, Yongguang Chen, Ge Dynamical Systems Multiagent Systems Adaptation and Self-Organizing Systems Physics and Society The behavior of one-dimensional Hegselmann-Krause (HK) dynamics driven by noise has been extensively studied. Previous research has indicated that within no matter the bounded or the unbounded space of one dimension, the HK dynamics attain quasi-synchronization (synchronization in noisy case) in finite time. However, it remains unclear whether this phenomenon holds in high-dimensional space. This paper investigates the random time for quasi-synchronization of multi-dimensional HK model and reveals that the boundedness and dimensions of the space determine different outcomes. To be specific, if the space is bounded, quasi-synchronization can be attained almost surely for all dimensions within a finite time, whereas in unbounded space, quasi-synchronization can only be achieved in low-dimensional cases (one and two). Furthermore, different integrability of the random time of various cases is proved. |
| title | Properties of Quasi-synchronization Time of High-dimensional Hegselmann-Krause Dynamics |
| topic | Dynamical Systems Multiagent Systems Adaptation and Self-Organizing Systems Physics and Society |
| url | https://arxiv.org/abs/2507.08900 |