Spectral stability and nonlinear cascades in specialized multilayer infrastructure networks

We develop a nonlinear multilayer network framework for finite-shock cascades in specialized infrastructure systems. The key distinction is between local stability around a pre-shock equilibrium and global resilience to finite perturbations. Local stability is governed by the spectral radius of the Jacobian, while sufficiently large shocks can generate widespread threshold exceedance even when the initial equilibrium remains locally stable. For nonnegative irreducible interaction matrices, Perron–Frobenius perturbation theory shows that stronger interlayer coupling increases the dominant spectral mode, whereas the effect of specialization depends on the alignment of weight reallocation with the left and right Perron eigenvectors rather than on concentration alone. Numerical experiments on stochastic six-layer networks directly implement these mechanisms. Within each Monte Carlo realization, the same base network is followed across the specialization and coupling grids, so changes in specialization represent a genuine matrix path. Shocks are one-time perturbations to the initial condition, with no post-failure redistribution or topology changes. Sixteen independent realizations are used per scenario. We report concentration, analytic and finite-difference Perron sensitivities, Jacobian-based stability diagnostics, dispersion across realizations, layer-specific responses, and parameter sensitivity. Locally stable equilibria can nonetheless exhibit large nonlinear responses to finite shocks, illustrating the local-to-global distinction.