Evaluation of Security System Effectiveness Based on Petri Nets and Ordinary Differential Equations

Security systems are essential for maintaining public safety and protecting critical assets, yet most existing evaluation approaches remain static, capture only partial interactions among assets, security systems, and offenders, and lack qualitative analyses of long-term stability. To address these limitations, this study introduces an integrated Petri net–ordinary differential equation framework that combines the discrete-event modeling strength of Petri nets with the continuous-time analysis capability of ordinary differential equations, thereby capturing the dynamic interplay among assets, security systems, and offenders and enabling equilibrium and stability analysis. Numerical simulations are conducted under different parameter settings to validate both the stability of the framework and the role of the security effectiveness parameter. The results demonstrate that enhancing this parameter improves protection capability, suppresses offender activity, reduces asset losses and promotes long-term system stability. By capturing interdependent dynamics within a unified model, the proposed approach advances beyond traditional methods and provides both a theoretical foundation and practical guidance for optimizing resource allocation and designing protection strategies.