Article

Evolution algebras and dynamical systems of a worm propagation model

Uygun JamilovV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, National University of Uzbekistan, Tashkent, UzbekistanM. LadraDepartment of Mathematics & Institute of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain

Linear and Multilinear Algebrajournal2021en

ABI

Abstract

We consider an evolution algebra identifying the coefficients of SIS–SIR worm propagation models as the structure constants of the algebra. The basic properties of this algebra are studied. We prove that it is a commutative (and hence flexible), not associative and baric algebra. We describe the full set of idempotent elements and the full set of absolute nilpotent elements. We find all the fixed points of the dynamical systems. We also study several properties of the algebra connecting them to dynamical systems.

Topics

Nonlinear Dynamics and Pattern Formation Advanced Topics in Algebra Algebraic structures and combinatorial models

Identifiers

DOI: 10.1080/03081087.2020.1864264

Citations and references

Cited by 036 references

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