Ordered avalanches on the Bethe Lattice
Authors:
- Malgorzata J. Krawczyk,
- Paweł Oświęcimka,
- Krzysztof Kułakowski,
- Stanisław Drożdż
Abstract
We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b, each of k out-neighbors gets one grain. The probability of an avalanche of size s is proportional to s −τ . When the avalanche mass is conserved (k = b), we get τ = 1. For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent τ is found to depend on the model parameters; τ ≈ log(b)/log(k). The distribution of the time duration of avalanches is exponential. Multifractal analysis of the avalanche sequences reveals their strongly non-uniform fractal organization. Maximal value of the singularity strength αmax in the bifractal spectrum is found to be 1/τ.
- Record ID
- CUT5e22d74d8c9d4a8fb16d17c877e394a2
- Publication categories
- ;
- Author
- Journal series
- Entropy, ISSN , e-ISSN 1099-4300, Monthly
- Issue year
- 2019
- Vol
- 21
- No
- 10
- Pages
- [1-13]
- Article number
- 968
- Other elements of collation
- rys.; wykr.; Bibliografia (na s.) - 11-13; Bibliografia (liczba pozycji) - 49; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 21, Iss. 10, Spec. Iss.
- Substantive notes
- Special Issue: Disordered Systems, Fractals and Chaos
- Keywords in English
- self-organized criticality, multifractals, mean field, social processes
- DOI
- DOI:10.3390/e21100968 Opening in a new tab
- URL
- https://www.mdpi.com/1099-4300/21/10/968 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 0
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT5e22d74d8c9d4a8fb16d17c877e394a2/
- URN
urn:pkr-prod:CUT5e22d74d8c9d4a8fb16d17c877e394a2
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.