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<p>To analyze the online computer user–hacker system, this paper develops a fractional-order model involving four populations: online computer users, hackers, the cybersecurity force, and the justice system. Dynamics of the system is studied in terms of boundedness, uniqueness, and existence of the solutions. Conditions determining the stability of different equilibrium points are expressed through specific threshold parameters. The logical involvement various parameters introduced in the model have been analyzed by sensitivity indices. Global stability of axial, cyber security force and justice system free and coexistence equilibrium points are studied. Influence of the various parameters have been analyzed with the help of transcritical bifurcation. To numerically verify our theoretical results, we proposed a new mathematical skill operational integration matrix constructed using the independence polynomial of graphs.</p>

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A modified fractional predator–prey model for user-hacker interaction in online computer networks

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Sindhu J. Achar,
  • T. Sathiyaraj,
  • S. Harshavarthini,
  • Ong Seng Huat

摘要

To analyze the online computer user–hacker system, this paper develops a fractional-order model involving four populations: online computer users, hackers, the cybersecurity force, and the justice system. Dynamics of the system is studied in terms of boundedness, uniqueness, and existence of the solutions. Conditions determining the stability of different equilibrium points are expressed through specific threshold parameters. The logical involvement various parameters introduced in the model have been analyzed by sensitivity indices. Global stability of axial, cyber security force and justice system free and coexistence equilibrium points are studied. Influence of the various parameters have been analyzed with the help of transcritical bifurcation. To numerically verify our theoretical results, we proposed a new mathematical skill operational integration matrix constructed using the independence polynomial of graphs.