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Article Dans Une Revue Discontinuity, Nonlinearity, and Complexity Année : 2016

Dynamical Systems Generated by a Gonosomal Evolution Operator

Utkir A Rozikov
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Résumé

In this paper we consider discrete-time dynamical systems generated by gonosomal evolution operators of sex linked inheritance. Mainly we study dynamical systems of a hemophilia, which biologically is a group of hereditary genetic disorders that impair the body's ability to control blood clotting or coagulation, which is used to stop bleeding when a blood vessel is broken. We give an algebraic model of the biological system corresponding to the hemophilia. The evolution of such system is studied by a nonlinear (quadratic) gonosomal operator. In a general setting, this operator is considered as a mapping from R n , n ≥ 2 to itself. In particular, for a gonosomal operator at n = 4 we explicitly give all (two) fixed points. Then limit points of the trajectories of the corresponding dynamical system are studied. Moreover we consider a normalized version of the gonosomal operator. In the case n = 4, for the normalized gonosomal operator we show uniqueness of fixed point and study limit points of the dynamical system.

Dates et versions

hal-03229619 , version 1 (21-05-2021)

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Utkir A Rozikov, Richard Varro. Dynamical Systems Generated by a Gonosomal Evolution Operator. Discontinuity, Nonlinearity, and Complexity, 2016, 5, pp.173 - 185. ⟨10.5890/dnc.2016.06.007⟩. ⟨hal-03229619⟩
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