Decoupling Transient Instability and Steady-State Persistence in Nonlinear Multi-Agent Influence Networks

Nonlinear aggregation mechanisms are increasingly deployed in distributed multi-agent systems, yet their stability properties remain poorly characterised beyond classical spectral analyses. We study a nonlinear influence–recovery model on undirected networks and demonstrate a fundamental structural decoupling between transient instability and steady-state persistence. Classical linear spectral theory predicts a single instability threshold governed by λmax(A); we prove analytically, using a Lyapunov function and a formal global stability theorem, and verify empirically that nonlinear aggregation systematically violates this prediction in a topology-dependent manner. We conduct experiments on four network types (Twitter, Reddit, citation, collaboration) using both publicly available SNAP graph datasets and synthetic graphs calibrated to match their documented structural statistics, six canonical topology models (star, Erdo˝ s–Re´nyi, Baraba´si–Albert, Watts–Strogatz, modular, dense), and compare our model against SIS epidemic dynamics, threshold cascade, and linear consensus. An ablation study isolates each parameter’s contribution, and an AI agent misinformation experiment with n=100 agents and bootstrap confidence intervals directly instantiates our theoretical claims on directed as well as undirected communication architectures. Our results establish that the two fragility modes are governed by fundamentally different structural mechanisms, with direct implications for the safety of distributed AI coordination architectures.