Scholarlink

<p>In this paper, we analyze a mathematical model designed to study the behavior of hackers. Despite significant efforts by various stakeholders in the field, the problem of hacking and the security of information systems remains a persistent challenge in the domain of Internet security. The proposed model is examined using the stability theory of nonlinear differential equations. Based on the outcomes of this analysis, we demonstrate the positivity of the solutions. The model admits two equilibrium points: one representing a hacking-free state, and the other corresponding to a state in which hacking persists. We verify the existence of these equilibrium points and analyze their local stability. By constructing an appropriate Lyapunov function and applying LaSalle’s invariance principle, we gain insights into the global stability of these equilibria under specific conditions. In addition, we compute the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( R_0 \)</EquationSource> </InlineEquation>, which quantifies the potential spread of hacking behavior in the system. To further enrich the model, we introduce optimal control strategies involving two types of interventions: an awareness and sensitization program, and a sanctioning policy aimed at discouraging malicious behavior. The Pontryagin Maximum Principle is employed to characterize the optimal control functions. To validate our theoretical results, numerical simulations were performed using a finite difference scheme implemented in MATLAB. The simulation outcomes confirm and illustrate the effectiveness and consistency of the theoretical findings presented in this study.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Mathematical modeling, analysis, and optimal control of hacker behavior in cybersecurity systems

  • 期刊论文

  • 发表日期：

    2025年12月1日

查看全文
  • Habib Hassouni,
  • Amine El Bhih,
  • Omar Balatif

摘要

In this paper, we analyze a mathematical model designed to study the behavior of hackers. Despite significant efforts by various stakeholders in the field, the problem of hacking and the security of information systems remains a persistent challenge in the domain of Internet security. The proposed model is examined using the stability theory of nonlinear differential equations. Based on the outcomes of this analysis, we demonstrate the positivity of the solutions. The model admits two equilibrium points: one representing a hacking-free state, and the other corresponding to a state in which hacking persists. We verify the existence of these equilibrium points and analyze their local stability. By constructing an appropriate Lyapunov function and applying LaSalle’s invariance principle, we gain insights into the global stability of these equilibria under specific conditions. In addition, we compute the basic reproduction number \( R_0 \) , which quantifies the potential spread of hacking behavior in the system. To further enrich the model, we introduce optimal control strategies involving two types of interventions: an awareness and sensitization program, and a sanctioning policy aimed at discouraging malicious behavior. The Pontryagin Maximum Principle is employed to characterize the optimal control functions. To validate our theoretical results, numerical simulations were performed using a finite difference scheme implemented in MATLAB. The simulation outcomes confirm and illustrate the effectiveness and consistency of the theoretical findings presented in this study.