This video presents a method to move the study of complex systems from an empirical stage to a predictive phenomenological framework. It starts from the Landau–Ginzburg equation for dissipative processes, introduces discrete-time feedback, and incorporates a power-law driving force to capture the onset of chaos or criticality. The approach yields an analytical nonlinear renormalization-group fixed-point map describing one-dimensional transitions to and from chaos, with its Lyapunov function corresponding to the thermodynamic potential in q-statistics.

The method is applied to key problems in complex systems, including self-organization, empirical laws such as Zipf and Kleiber laws, network and game-theoretic methods, and phenomena in condensed matter and related fields, such as critical fluctuations, glass formation, and localization transitions.