Delayed Fractional-Order Graph Dynamics for Cascade Escalation and Reconfiguration Failure in Integrated Modular Avionics

Integrated Modular Avionics (IMA) integrates safety-critical functions on shared computing and network resources, creating coupling channels through which a local fault may escalate into a catastrophic system-level scenario. This study develops a graph-based fractional-order model for cascade escalation in IMA architectures with communication delays and reconfiguration failures. The architecture is represented as a weighted directed graph of core processing modules, network switches, and remote data concentrators, where each node carries functional degradation and queue-backlog states. The proposed delayed Caputo fractional-order dynamics incorporate degradation propagation, backlog spillover, mixed-criticality priority conflict, and a state-dependent reconfiguration-failure mechanism. We establish well-posedness and positive invariance of the feasible state domain, derive a sufficient cascade threshold that separates a delay-independent, globally Mittag–Leffler stable nominal regime from a supercritical regime in which bistability and catastrophic attractors may occur, and characterize delay-induced oscillatory instability together with a memory-stabilization effect. Numerical experiments on a synthetic 22-node IMA configuration show fault absorption below the threshold, reconfiguration-contained cascades under sufficient supervisory capacity, and global escalation when reconfiguration collapses under load. The results indicate that backlog growth is an early warning signal and that maintaining the cascade threshold below unity while provisioning reconfiguration capacity above the tipping point can support safer reconfiguration-policy design in certifiable avionics.