Strictly non-volterra Quadratic Stochastic Operator (QSO) on 3-dimensional simplex

• Main Authors: Ganikhodjaev, Nasir, Jusoo, Siti Hasana
• Format: Article
• Language: English; English; English
• Published: Institute of Physics Publishing 2018
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/66206/1/66206_Strictly%20non-Volterra%20quadratic%20stochastic.pdf; http://irep.iium.edu.my/66206/2/66206_Strictly%20non-Volterra%20quadratic%20stochastic_SCOPUS.pdf; http://irep.iium.edu.my/66206/3/66206_Strictly%20non-Volterra%20quadratic%20stochastic_WOS.pdf; http://irep.iium.edu.my/66206/; https://aip.scitation.org/doi/abs/10.1063/1.5041664?journalCode=apc

In this paper, we investigate the dynamics of the Lebesque quadratic stochastic operator on the set of all Lebesque measures of the set X = [0,1] . We consider the family of functions such that for any fixed x, y a probability measure P(x, y,.) is absolutely continuous with respect to usual Lebesque measure on X with simple Radon-Nikodym derivative. We construct the family of strictly non-Volterra quadratic stochastic and show that their dynamic behavior coincides with dynamic of strictly non-Volterra quadratic stochastic operator on 3-dimensional simplex.