Salcedo-Sanz, S.Casillas-Pérez, D.Del Ser, J.Casanova-Mateo, C.Cuadra, L.Piles, M.Camps-Valls, G.2022-04-29Salcedo-Sanz , S , Casillas-Pérez , D , Del Ser , J , Casanova-Mateo , C , Cuadra , L , Piles , M & Camps-Valls , G 2022 , ' Persistence in complex systems ' , Physics Reports , vol. 957 , pp. 1-73 . https://doi.org/10.1016/j.physrep.2022.02.0020370-1573researchoutputwizard: 11556/1277Publisher Copyright: © 2022 The Author(s)Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems’ persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature review is also carried out. We also present and discuss some relevant results on persistence, and give empirical evidence of performance in different detailed case studies, for both short-term and long-term persistence. A perspective on the future of persistence concludes the work.736222921enginfo:eu-repo/semantics/openAccessjournal article10.1016/j.physrep.2022.02.002PersistenceComplex systemsSystems’ statesLong-term and short-term methodsAtmosphere and climateRenewable energyEconomyComplex networksOptimization and planningMachine learningNeural networksNeuroscienceMemoryAdaptationPersistenceComplex systemsSystems’ statesLong-term and short-term methodsAtmosphere and climateRenewable energyEconomyComplex networksOptimization and planningMachine learningNeural networksNeuroscienceMemoryAdaptationGeneral Physics and AstronomySDG 7 - Affordable and Clean EnergyProject IDinfo:eu-repo/grantAgreement/EC/H2020/647423/EU/Statistical Learning for Earth Observation Data Analysis/SEDALinfo:eu-repo/grantAgreement/EC/H2020/647423/EU/Statistical Learning for Earth Observation Data Analysis/SEDALFunding InfoThis research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423).This research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423).http://www.scopus.com/inward/record.url?scp=85125263184&partnerID=8YFLogxK