{"title":"Time-series thresholding and avalanche dynamics in networks of the critical branching process.","authors":"Lei Tao, Sheng-Jun Wang, Zi-Gang Huang","doi":"10.1103/PhysRevE.111.044129","DOIUrl":null,"url":null,"abstract":"<p><p>Avalanche sizes and durations following power-law distributions are observed in many systems and are considered hallmarks of criticality. Time-series thresholding is a commonly used method to define avalanches, but this method is controversial. In this study, we use the time-series thresholding method to define avalanches and investigate the statistical properties of avalanches in the Kinouchi-Copelli (KC) model. We consider two definitions of avalanche size, (1) total area above threshold value reference and (2) total area above zero, and then analyze the size and duration distributions. Our results show that while avalanche size and duration obey a power-law distribution, the exponents of size and duration differ from those of the critical branching process. The scaling relation holds for avalanches defined by the first method but fails for those avalanches tdefined by the second. This study provides new insights into avalanche definition methods and avalanche distribution exponents in continuous time-series.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"111 4-1","pages":"044129"},"PeriodicalIF":2.4000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.111.044129","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Avalanche sizes and durations following power-law distributions are observed in many systems and are considered hallmarks of criticality. Time-series thresholding is a commonly used method to define avalanches, but this method is controversial. In this study, we use the time-series thresholding method to define avalanches and investigate the statistical properties of avalanches in the Kinouchi-Copelli (KC) model. We consider two definitions of avalanche size, (1) total area above threshold value reference and (2) total area above zero, and then analyze the size and duration distributions. Our results show that while avalanche size and duration obey a power-law distribution, the exponents of size and duration differ from those of the critical branching process. The scaling relation holds for avalanches defined by the first method but fails for those avalanches tdefined by the second. This study provides new insights into avalanche definition methods and avalanche distribution exponents in continuous time-series.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.