Complex Systems were identified and studied in different fields, such as physics, biology, and economics. These systems exhibit exciting properties such as self-organization, robust order, and emergence. In recent years, software systems displaying behaviors associated with Complex Systems are starting to appear, and these behaviors are showing previously unknown potential (e.g., GPT-based applications). Yet, there is no commonly shared definition of a Complex Software System that can serve as a key reference for academia to support research in the area. In this paper, we adopt the theory-to-research strategy to extract properties of Complex Systems from research in other fields, mapping them to software systems to create a formal definition of a Complex Software System. We support the evolution of the properties through future validation, and we provide examples of the application of the definition. Overall, the definition will allow for a more precise, consistent, and rigorous frame of reference for conducting scientific research on software systems.

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