2015/04/20 by Rozikov, U. A., Varro, R.
#17D92 #17D99 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1504.05109
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 \mathbb Rn, 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.