Persistence in Complex Systems

TL;DR

This paper provides a comprehensive review of persistence in complex systems, covering definitions, methods, literature, and empirical case studies for both short-term and long-term persistence, highlighting recent advances and future directions.

Contribution

It offers a thorough synthesis of current concepts, methods, and empirical findings on persistence in complex systems, including new case study analyses.

Findings

Empirical evidence of persistence in various systems

Comparison of methods for short-term and long-term persistence

Identification of future research directions

Abstract

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.