A Relational Dynamical Systems Model for Coherence Optimization in Complex Networks

We introduce a formal relational dynamical systems framework for regulating global coherence in complex adaptive networks. By applying a non-linear threshold-gating mechanism derived from a modulated trace-map recurrence, we demonstrate that a system can optimize its stability against stochastic perturbation. We prove that under a uniform geometric protection threshold bound by the golden ratio ϕ = (1 + √5)/2, the system forms a contractive space that converges monotonically to a unique structural equilibrium, mitigating destructive resonance and forcing global network synchronization.