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<p>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.</p>

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An effective evaluation framework for security systems using ordinary differential equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月3日

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  • Yishuai Liu,
  • Songbai Guo,
  • Tieying Wang,
  • Hua Jin

摘要

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.