Assessing multidimensional resilience using an eigenvalue-based local linear dynamic model: a case study of Hangzhou Bay coast zone, China

Coastal zones are critical regions for ecological protection, socioeconomic development, and disaster risk reduction. Coastal resilience assessment requires not only the measurement of overall resilience levels, but also the analysis of temporal relationships among different resilience-related capacities. This study develops an eigenvalue-based local linear dynamic model for assessing multidimensional coastal resilience. Stability, recoverability, and transformability are used as aggregate state variables to characterize the capacity of a coastal social-ecological system to maintain essential functions, recover after disturbances, and adapt to long-term changes. Composite scores for the three resilience dimensions are first constructed. A local linear state matrix is then estimated to describe the fitted temporal relationships among these aggregate state variables, and eigenvalue analysis is used to characterize local recovery dynamics around an empirical reference state. Compared with conventional indicator-weighting approaches, the proposed model provides a mathematical and dynamic perspective for examining multi-dimensional coastal resilience. The eigenvalue-based results are interpreted in terms of local recovery dynamics under the adopted local linear approximation. In the Hangzhou Bay case, the model is applied using annual indicator data from 2010 to 2023. The results show that stability, recoverability, and transformability generally improved during the study period, but their temporal trajectories differed. Eigenvalue analysis indicates that the fitted system remained locally stable under the adopted linear approximation, while the dominant recovery mode was relatively slow, suggesting a slow local recovery mode in the fitted system. Sensitivity analysis, multicollinearity diagnostics, a quadratic robustness check, and an external consistency check using disaster-related economic loss further support the robustness and interpretability of the results. Overall, this study provides a quantitative model for assessing multidimensional coastal resilience by linking indicator-based composite assessment with local linear dynamic modeling and eigenvalue analysis.