Szczegóły publikacji
Opis bibliograficzny
Perfect cycles in the synchronous Heider dynamics in complete network / Zdzisław BURDA, Małgorzata J. KRAWCZYK, Krzysztof KUŁAKOWSKI // Physical Review. E ; ISSN 2470-0045. — Tytuł poprz.: Physical Review E, Statistical, nonlinear, and soft matter physics ; ISSN: 1539-3755. — 2022 — vol. 105 iss. 5 art. no. 054312, s. 054312-1–054312-6. — Bibliogr. s. 054312-5–054312-6. — Publikacja dostępna online od: 2022-05-20
Autorzy (3)
Dane bibliometryczne
| ID BaDAP | 140497 |
|---|---|
| Data dodania do BaDAP | 2022-06-14 |
| Tekst źródłowy | URL |
| DOI | 10.1103/PhysRevE.105.054312 |
| Rok publikacji | 2022 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Physical Review, E |
Abstract
We discuss a cellular automaton simulating the process of reaching Heider balance in a fully connected network. The dynamics of the automaton is defined by a deterministic, synchronous, and global update rule. The dynamics has a very rich spectrum of attractors including fixed points and limit cycles, the length and number of which change with the size of the system. In this paper we concentrate on a class of limit cycles that preserve energy spectrum of the consecutive states. We call such limit cycles perfect. Consecutive states in a perfect cycle are separated from each other by the same Hamming distance. Also the Hamming distance between any two states separated by k steps in a perfect cycle is the same for all such pairs of states. The states of a perfect cycle form a very symmetric trajectory in the configuration space. We argue that the symmetry of the trajectories is rooted in the permutation symmetry of vertices of the network and a local symmetry of a certain energy function measuring the level of balance and frustration of triads.
