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

Hoang, Manh Tuan

doi:10.1007/s12346-021-00516-3

Cited by 7 publications

(2 citation statements)

References 46 publications

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“…This topic has strongly attracted the attention of mathematicians and engineers for many years (see, for instance, [1,9,28,31,[33][34][35] and references therein). Recently, we have studied qualitative properties and reliable numerical schemes for some mathematical models of computer viruses and malware [5,[12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses

Tuan¹,

Thu²

2023

ISJ

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Abstract— The aim of this work is to construct high-order numerical schemes that preserve the dynamical properties of a mathematical model describing the spread of computer viruses on the Internet. For this purpose, we first apply Mickens’ methodology to formulate a dynamically consistent nonstandard finite difference (NSFD) scheme for the model under consideration. After that, the constructed NSFD scheme is combined with Richardson’s extrapolation method to generate higher-accuracy numerical approximations. The result is that we obtain extrapolated numerical schemes that not only preserve the dynamical properties of the computer virus propagation model but also provide higher-accuracy numerical approximations. In addition, a set of numerical examples is conducted to illustrate and support the theoretical findings and to show the advantages of the proposed numerical schemes.

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Section: Introductionmentioning

confidence: 99%

Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses

Tuan¹,

Thu²

2023

ISJ

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“…It was proved in many recognized works that fractionalorder models can describe phenomena and processes arising in real-world applications more accurately than integer-order models due to the effective memory function of fractional derivatives [4,5,6,7,37,39,49,51,72,73,74,79,80]. Recently, we have considered some fractional-order systems that mathematically model phenomena and processes arising in biology and ecology, in which the stability problem was mainly focused [41,42].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and numerical simulation of a new fractional-order two-stage species model with recruitment

Hoang

2023

Preprint

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The purpose of this work is to propose and analyze a new fractional-order two-stage species model with recruitment to discover memory effects on population dynamics. This fractional-order model is constructed by incorporating a well-known integer-order two-stage species model with the Caputo fractional derivative. Firstly, the positivity and boundedness of solutions of the proposed model are investigated by using some standard comparison results for fractional differential equations. Next, a simple approach is utilized to study stability properties of the fractional-order model. This approach is based on the Lyapunov stability theory and Barbalat’s lemma in combination with some nonstandard techniques for fractional dynamical systems. More clearly, we use general quadratic Lyapunov candidate functions and combine them with characteristics of quadratic forms associated with real matrices to establish the stability properties. As an important consequence, global asymptotic stability, uniform and Mittag-Leffler stability and therefore, population dynamics of the proposed fractional-order model are analyzed rigorously. Finally, we extend the Mickens’ methodology to construct a dynamically consistent nonstandard finite difference (NSFD) scheme for the purpose of numerical simulation of the fractional-order model. It is proved that the NSFD scheme preserves the positivity and boundedness of the fractional-order model regardless of the values of the step size; moreover, it is also simple and efficient. The theoretical results and advantages of the NSFD scheme are supported by illustrative numerical experiments. The experiments provide strong evidence, which shows that the numerical results are consistent with the theoretical ones.

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Dynamics of a fractional-order epidemiological model for computer viruses

Hoang

2023

São Paulo J. Math. Sci.

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

Cited by 7 publications

References 46 publications

Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses

Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses

Dynamical analysis and numerical simulation of a new fractional-order two-stage species model with recruitment

Dynamics of a fractional-order epidemiological model for computer viruses

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