Modern physical protection systems (PPSs) play a pivotal role in safeguarding critical infrastructure and maintaining public safety. Yet increasingly complex system architectures and evolving threat landscapes pose significant vulnerability challenges to PPSs. Conventional vulnerability assessment methods predominantly rely on expert knowledge or single-path analysis, which inadequately captures complex inter-component relationships and the impact of uncertainties on PPS vulnerabilities. To bridge this gap, this paper introduces a hybrid analytical framework synergizing complex network theory with fuzzy Petri net (FPN). The proposed method operates through two integrated phases: (1) constructing topological models of PPS using complex network theory to characterize component interrelationships, and (2) incorporating FPN to establish vulnerability propagation models that simulate cascading effects and quantify overall system vulnerability. Compared with conventional methods, the proposed approach demonstrates superior effectiveness in identifying critical vulnerability points within the system, providing a scientifically grounded foundation for enhancing PPS security and implementing risk control measures.

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.

Security systems play a crucial role in safeguarding individuals, their personal belongings, and properties. The effectiveness of a security system depends largely on prudent investment and proper implementation, thereby ensuring the comprehensive protection of property owners’ lives and assets. This paper introduces a three-dimensional ordinary differential equations (ODEs) dynamic model that characterizes the offensive and defensive interactions among property owners, criminals, and security systems. From a mathematical perspective, we analyze the global dynamical behavior of the model and employ numerical simulations to explore the interactions among the three entities. Theoretical analysis and simulation results confirm that the ODEs model effectively captures the offense-defense dynamics among the involved parties. Furthermore, by applying real-world social data in the numerical simulations, the model’s validity is empirically verified. Through an examination of how variations in key parameters affect property owners, criminals, and security systems, this study proposes actionable recommendations to enhance the performance of security systems in protecting property owners from criminal threats.