Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


The Global Attractiveness of the Fixed Point of a Gonosomal Evolution Operator

Discontinuity, Nonlinearity, and Complexity 10(1) (2021) 143--149 | DOI:10.5890/DNC.2021.03.010

Akmal T. Absalamov

Samarkand State University, Boulevard str., 140104, Samarkand, Uzbekistan

Download Full Text PDF

 

Abstract

In the paper we prove a conjecture of U.A. Rozikov and R. Varro about globally attractiveness of a unique nonhyperbolic fixed point of the normalized gonosomal evolution operator of a sex linked inheritance.

References

  1. [1]  Baca\"er, N. (2011), A short history of mathematical population dynamics, Springer-Verlag London, Ltd., London.
  2. [2]  Ganikhodzhaev, R.N., Mukhamedov, F.M., and Rozikov, U.A. (2011), { Quadratic stochastic operators and processes: results and open problems}, Inf. Dim. Anal. Quant. Prob. Rel. Fields, 14(2), 279-335
  3. [3]  Kesten, H. (1970), Quadratic transformations: A model for population growth, I, II, Adv. Appl. Probab., 2(2), 1-82; 179-228.
  4. [4]  Lyubich Y.I. { Mathematical structures in population genetics}. Springer-Vergar, Berlin (1992)
  5. [5]  Rozikov, U.A. (2013), { Evolution operators and algebras of sex linked inheritance,} Asia Pacific Math. Newsletter, 3(1), 6-11.
  6. [6]  Varro, R. (2016), { Gonosomal algebra,} Jour. Algebra, 447, 1-30.
  7. [7]  Ladra, M. and Rozikov, U.A. (2013), { Evolution algebra of a bisexual population}, Jour. Algebra, 378, 153-172.
  8. [8]  Reed, M.L. (1997), { Algebraic structure of genetic inheritance,} Bull. Amer. Math. Soc. (N.S.), 34(2), 107-130.
  9. [9]  Rozikov, U.A. and Zhamilov, U.U. (2011), {Volterra quadratic stochastic operators of bisexual population,} Ukraine Math. Jour., 63(7), 985-998.
  10. [10]  Absalamov, A.T. and Rozikov U.A. (2020), The dynamics of gonosomal evolution operators, Jour. Applied Nonlinear Dynamics, 9(2), 247-257.
  11. [11]  Rozikov, U.A. and Varro R. (2016), { Dynamical systems generated by a gonosomal evolution operator,} Discontinuity, Nonlinearity and Complexity, 5, 173-185