Abstract

Complexity typically manifests as nonlinear relationships between the whole and parts of a system. Chaos emerges through nonlinear evolutionary processes, while emergence arises when the system develops characteristics absent in its components. By analyzing relationships between set-theoretic elements, this paper explores fundamental system theory issues. Based on the premise of a vicious cycle between collective and individual existence, the study derives core relationships governing system evolution, clarifies consistency in system transformation, and identifies the origins of complexity in chaotic and emergent phenomena.