This work presents a theoretical framework for the response of nonlinear networks to weak external forcing near criticality. Modeling the system as a stochastic nonlinear oscillator subject to thermal noise and a low-amplitude periodic drive, we analyze the dynamics using concepts from Landau theory and stochastic resonance. We show that as the system approaches a critical point, the effective restoring force vanishes and the susceptibility diverges, dramatically enhancing sensitivity to otherwise negligible external signals. In this regime, weak exogenous forcing acts as a symmetry-breaking field, biasing the probabilistic landscape and influencing the selection of macroscopic states during structural reorganization. The results provide a physically grounded perspective on the extreme sensitivity of critically balanced systems to sub-thermal perturbations in non-equilibrium conditions.
Claudia Attaianese (Tue,) studied this question.