Complexity synchronization as a diagnostic and control principle for adaptive systems

Abstract: Adaptive systems can exhibit similar levels of performance while relying on fundamentally different internal modes of coordination. Standard metrics such as average cooperation or payoff indicate whether a system succeeds, but do not reveal how coordination is organized across interacting components or which adaptive variables should be targeted when performance fails. Here we propose complexity synchronization (CS), the synchronization of evolving temporal complexity across coupled variables, as a diagnostic and intervention guiding principle for adaptive systems. We test this idea in an adaptive multi agent system composed of Selfish Algorithm agents interacting in a reduced Predator Prey model with a Prisoners Dilemma like payoff structure. Temporal complexity is quantified using sliding window modified diffusion entropy analysis (MDEA) and detrended fluctuation analysis (DFA). CS is defined as the correlation between the resulting time dependent scaling exponents. In the high-interaction regime, MDEA-based CS increases with cooperative performance, whereas DFA based CS captures a distinct persistence dominated coordination mode. Our results show that CS can reveal functionally relevant subsystems and provide a principled basis for targeted repair. More broadly, CS offers a general diagnostic and engineering framework for understanding and controlling coordination in biological, social, human machine, and other adaptive systems.