Iterative Macroscopic Coherence in Driven Nonlinear Networks: Structural Memory and Adaptive Emergence via Endogenous Expansion

This work presents a theoretical framework for iterative structural adaptation in closed nonlinear dynamical systems under repeated external forcing. We model the system as a network of globally coupled nonlinear oscillators subject to sequential parametric perturbations. Using a Kuramoto-like formulation, we show that unbounded energy growth can be avoided through an endogenous damping mechanism proportional to the fractional expansion rate of an effective macroscopic phase space volume. This dynamic expansion acts as an internal heat sink, enabling finite-time phase synchronization and a significant reduction in relational entropy at each cycle. Successive perturbation-condensation cycles yield a sequence of coherent macroscopic states, each characterized by a distinct collective frequency. These emergent frequencies can be associated with mass-like effective inertias in a dynamical sense, providing a mechanism for structural memory. When perturbations exceed effective dynamical limits, the system undergoes structural dissolution and transitions toward a highly mixed state. This establishes a dynamical boundary between adaptive self-organization and loss of macroscopic coherence. The results suggest a physically motivated pathway for adaptive robustness, structural memory, and self-organization in isolated complex systems, with conceptual connections to coarse-grained descriptions of emergent classicality.