Abstract

Abstract for: Parameter-Based Eigenvalue Elasticity Analysis for Stock-and-Flow Models in a Categorical Framework

Introduction Classical eigenvalue-based analyses in system dynamics typically focus on dominant modes or structural interpretations, limiting their ability to capture parameter-driven behavior in nonlinear and time-varying systems. This creates a gap in understanding how model parameters influence system dynamics, particularly near regime transitions, oscillatory behavior, and non-equilibrium conditions.
Approach This work develops a categorical framework for parameter-based eigenvalue sensitivity analysis using ACSet-encoded stock-and-flow models. Building on prior formulations, eigenvalues are treated as implicit functions of parameters through the Jacobian. The approach systematically computes sensitivities across all modes, leveraging compositional system dynamics representations.
Results Results demonstrate that parameter influence varies significantly across dynamical regimes and is often not captured by dominant eigenvalue analysis alone. The method reveals informative sensitivity signals in oscillatory and near-zero regimes, where traditional approaches fail, and provides consistent insights across different model configurations, including SIRS systems.
Discussion The findings highlight the importance of parameter-based sensitivity analysis in understanding nonlinear system behavior beyond structural interpretations. By integrating categorical representations with eigenvalue sensitivity theory, this work offers a robust analytical framework applicable to complex, time-varying systems and supports more reliable interpretation of model dynamics.

Introduction	Classical eigenvalue-based analyses in system dynamics typically focus on dominant modes or structural interpretations, limiting their ability to capture parameter-driven behavior in nonlinear and time-varying systems. This creates a gap in understanding how model parameters influence system dynamics, particularly near regime transitions, oscillatory behavior, and non-equilibrium conditions.
Approach	This work develops a categorical framework for parameter-based eigenvalue sensitivity analysis using ACSet-encoded stock-and-flow models. Building on prior formulations, eigenvalues are treated as implicit functions of parameters through the Jacobian. The approach systematically computes sensitivities across all modes, leveraging compositional system dynamics representations.
Results	Results demonstrate that parameter influence varies significantly across dynamical regimes and is often not captured by dominant eigenvalue analysis alone. The method reveals informative sensitivity signals in oscillatory and near-zero regimes, where traditional approaches fail, and provides consistent insights across different model configurations, including SIRS systems.
Discussion	The findings highlight the importance of parameter-based sensitivity analysis in understanding nonlinear system behavior beyond structural interpretations. By integrating categorical representations with eigenvalue sensitivity theory, this work offers a robust analytical framework applicable to complex, time-varying systems and supports more reliable interpretation of model dynamics.