Classification of a new subclass of \(\xi^{(as)}\)-QSO and its dynamics
-
1990
Downloads
-
3936
Views
Authors
Izzat Qaralleh
- Department of Mathematics, Tafila Technical University, P. O. Box 179. zip code 66110, Tafila, Jordan
Abstract
A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This subject has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. In this paper we introduce a new subclass of \(\xi^{(as)}\)-QSO defined on 2D simplex. first we classify this subclass into 18 non-conjugate classes. Furthermore, we investigate the behavior of one class.
Share and Cite
ISRP Style
Izzat Qaralleh, Classification of a new subclass of \(\xi^{(as)}\)-QSO and its dynamics, Journal of Mathematics and Computer Science, 17 (2017), no. 4, 535-544
AMA Style
Qaralleh Izzat, Classification of a new subclass of \(\xi^{(as)}\)-QSO and its dynamics. J Math Comput SCI-JM. (2017); 17(4):535-544
Chicago/Turabian Style
Qaralleh, Izzat. "Classification of a new subclass of \(\xi^{(as)}\)-QSO and its dynamics." Journal of Mathematics and Computer Science, 17, no. 4 (2017): 535-544
Keywords
- Quadratic stochastic operator
- \(\ell\)-Volterra quadratic stochastic operator
- \(\xi^{(s)}\)-quadratic stochastic operator
- permuted \(\ell\)-Volterra quadratic stochastic operator
- dynamics
MSC
- 37E99
- 37N25
- 39B82
- 47H60
- 92D25
References
-
[1]
E. Akin, V. Losert, Evolutionary dynamics of zero-sum games, J. Math. Biol., 20 (1984), 231–258.
-
[2]
S. Bernstein, Solution of a mathematical problem connected with the theory of heredity, Ann. Math. Statistics, 13 (1942), 53–61.
-
[3]
R. N. Ganikhodzhaev , Quadratic stochastic operators, Lyapunov functions and tournaments, Russian Acad. Sci. Sb. Math., 76 (1993), 489–506.
-
[4]
R. N. Ganikhodzhaev, A chart of fixed points and Lyapunov functions for a class of discrete dynamical systems, Math. Notes., 56 (1994), 1125–1131.
-
[5]
N. N. Ganikhodzhaev, R. N. Ganikhodjaev, U. U. Jamilov, Quadratic stochastic operators and zero-sum game dynamics, Ergodic Theory Dynam. Systems, 35 (2015), 1443–1473.
-
[6]
R. Ganikhodzhaev, F. Mukhamedov, U. Rozikov, Quadratic stochastic operators and processes: results and open problems, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 14 (2011), 279–335.
-
[7]
R. Ganikhodzhaev, M. Saburov, K. Saburov, Schur monotone decreasing sequences, AIP Conf. Proc., 1575 (2013), 108–111.
-
[8]
R. D. Jenks, Quadratic differential systems for interactive population models, J. Differential Equations, 5 (1969), 497–514.
-
[9]
Y. L. Lyubich , Mathematical structures in population genetics, Springer-Verlag, Berlin (1992)
-
[10]
F. Mukhamedov, A. F. Embong, On b-bistochastic quadratic stochastic operators, J. Inequal. Appl., 2015 (2015 ), 16 pages.
-
[11]
F. Mukhamedov, N. Ganikhodjaev, Quantum Quadratic Operators and Processes, Springer, Berlin (2015)
-
[12]
F. Mukhamedov, A. H. M. Jamal, On \(\xi^{s}\)-quadratic stochastic operators in 2-dimensional simplex, Proceedings of the 6th IMT-GT Conference on Mathematics, 2010 (2010 ), 14 pages.
-
[13]
F. Mukhamedov, I. Qaralleh, W. N. F. A. W. Rozali, On \(\xi^{a}\)-quadratic stochastic operators on 2D simplex, Sains Malaysiana, 43 (2014), 1275–1281.
-
[14]
F. Mukhamedov, M. Saburov, On homotopy of volterrian quadratic stochastic operator, Appl. Math. Inf. Sci., 4 (2010), 47–62.
-
[15]
F. Mukhamedov, M. Saburov, A. H. M. Jamal, On dynamics of \(\xi^s\)-quadratic stochastic operators, Inter. Jour. Modern Phys., 9 (2012), 299–307.
-
[16]
F. Mukhamedov, M. Saburov, I. Qaralleh, Classification of \(\xi^{(s)}\)-Quadratic Stochastic Operators on 2D simplex, J. Phys. Conf. Ser., 2013 (2013 ), 9 pages.
-
[17]
F. Mukhamedov, M. Saburov, I. Qaralleh, On \(\xi^{(s)}\)-quadratic stochastic operators on two dimensional simplex and their behavior, Abstr. Appl. Anal., 2013 (2013 ), 12 pages.
-
[18]
M. Plank, Hamiltonian structures for the n-dimensional Lotka-Volterra equations, J. Math. Phys. , 36 (1995), 3520–3543.
-
[19]
U. A. Rozikov, A. Zada, On \(\ell\)- Volterra Quadratic stochastic operators, Int. J. Biomath., 3 (2010), 143–159.
-
[20]
U. A. Rozikov, A. Zada, \(\ell\)-Volterra quadratic stochastic operators: Lyapunov functions, trajectories,, Appl. Math. Inf. Sci., 6 (2012), 329–335.
-
[21]
U. A. Rozikov, U. U. Zhamilov, F-quadratic stochastic operators, Math. Notes., 83 (2008), 554–559.
-
[22]
M. Saburov, Dynamics of Double Stochastic Operators, J. Phys. Conf. Ser., 2016 (2016), 9 pages.
-
[23]
F. E. Udwadia, N. Raju, Some global properties of a pair of coupled maps: quasi-symmetry, periodicity and syncronicity , Phys., 111 (1998), 16–26.
-
[24]
S. M. Ulam, Problems in Modern mathematics, Wiley, New York (1964)
-
[25]
M. I. Zakharevic, The behavior of trajectories and the ergodic hypothesis for quadratic mappings of a simplex, Uspekhi Mat. Nauk, 33 (1978), 207–208.