Innovation–Distress Coupling in Multiplex Industrial Networks: Knowledge Diffusion, Failure Risk, and Spectral Thresholds

Innovation can strengthen industrial resilience, but in interconnected networks, it may also create financial fragility. This paper develops a coupled nonlinear multiplex-network model in which financial distress and effective knowledge evolve on risk-propagation and knowledge-diffusion layers. Innovation success depends on firm capability, industry conditions, and accessible knowledge; success lowers susceptibility and strengthens recovery, whereas failure adds distress pressure. We establish positive invariance and well-posedness. For the source-free knowledge and conditional unforced distress subsystems, global threshold results show extinction at or below the corresponding spectral threshold and a unique positive equilibrium above it. For the fully coupled unforced system, comparison arguments provide sufficient extinction and persistence bounds. We further show that improved knowledge weakly lowers the conditional financial distress persistence threshold and we derive a local innovation–failure boundary. Extended simulations examine directed asymmetry, rank alignment, edge overlap, and numerical and parameter uncertainty. Capability and supportive industry conditions reduce long-run distress, failure losses attenuate innovation benefits, and favorable knowledge-capability allocation among structurally influential firms is associated with greater resilience. These findings are model-generated mechanisms rather than empirically identified policy optima.