{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:48:11Z","timestamp":1760240891304,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T00:00:00Z","timestamp":1570060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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  \u2212 \u03c4     . When the avalanche mass is conserved (    k = b    ), we get     \u03c4 = 1    . For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent    \u03c4    is found to depend on the model parameters;     \u03c4 \u00a0 \u2248 \u00a0 l o g ( b ) \/ l o g ( 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     \u03b1  m a x      in the bifractal spectrum is found to be     1 \/ \u03c4    .<\/jats:p>","DOI":"10.3390\/e21100968","type":"journal-article","created":{"date-parts":[[2019,10,4]],"date-time":"2019-10-04T04:12:52Z","timestamp":1570162372000},"page":"968","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Ordered Avalanches on the Bethe Lattice"],"prefix":"10.3390","volume":"21","author":[{"given":"Malgorzata J.","family":"Krawczyk","sequence":"first","affiliation":[{"name":"Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. 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