Lyapunov Functions for Investigating Stability Properties of a Fractional-Order Computer Virus Propagation Model

• Hoang, Manh Tuan ^[1]
  1. [1] FPT University

     FPT University

     Vietnam

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
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• Resumen

  • The aim of this work is to formulate and study a fractional-order computer virus propagation model, which is derived from the Caputo fractional derivative and a recognized system of ordinary differential equations. Firstly, standard comparison results for fractional differential equations are used to establish the positivity and boundedness of solutions of the model. Secondly, we propose a simple and unified approach to investigate stability properties including the local and global asymptotic stability and uniform stability of the fractional-order model. This approach is based on the construction of appropriate Lyapunov functions in combination with the fractional order Barbalat’s lemma. Consequently, the stability properties and dynamics of the model are established rigorously. Lastly, a set of numerical examples is performed to support and illustrate the theoretical results. The examples show that the numerical results are consistent with theoretical ones.