Cascade Failure Thresholds: Admissibility Limits in Complex Networked Systems

Many complex systems consist of interconnected components whose behaviour depends on the stability of interactions across the entire network. When local disturbances exceed certain limits, failures may propagate across these interconnected systems, producing cascading disruption. Examples include electrical grid failures, financial contagion, ecosystem collapse, and supply chain breakdowns. This paper interprets cascade failure thresholds within the Paton System framework as admissibility limits governing the persistence of complex networked systems. Cascading failure occurs when system interactions exceed structural compatibility limits, allowing disturbances to propagate across network connections. Understanding cascade failure thresholds through admissibility provides a structural interpretation of systemic instability across interconnected systems.