Abnormal cascading dynamics in spatial networks driven by distance-shell-based diffusion and weight-driven load redistribution

In this work, we develop a new cascading failure model for spatial infrastructure networks by incorporating a distance-shell-based diffusion mechanism and a weight-driven load allocation rule into the load redistribution process. Specifically, when failures occur, disrupted loads are first redistributed across discrete distance shells according to a tunable distance-decay function, and are then allocated within each shell based on heterogeneous node weights, capturing the distance-dependent and attraction-driven behaviors commonly observed in real spatial systems. The proposed framework is governed by three interpretable parameters: the distance preference γ, the node-weight preference α, and the tolerance parameter β, which jointly control spatial localization, hub-oriented bias, and overload endurance. Systematic simulations on three real-world networks (London transport, Shanghai road, and US airport network) reveal robust abnormal cascading patterns. Increasing α consistently weakens robustness by amplifying load concentration on critical edges and intensifying redistribution shocks during cascade propagation. Increasing γ further strengthens spatial localization by contracting the effective diffusion radius and increasing load heterogeneity, with the dominant mechanism depending on network structure. Notably, the tolerance parameter β induces a non-monotonic robustness response, yielding a capacity paradox: while higher tolerance delays early-stage fragmentation, it preserves connectivity that funnels redistributed loads onto a small set of critical rerouting backbones, ultimately triggering abrupt overload clusters and enlarging the final failure scale. These findings highlight that cascading vulnerability is strongly shaped by structured redistribution behavior and suggest that resilience enhancement should prioritize long-range routing redundancy and targeted reinforcement of critical rerouting backbones.