Sains Malaysiana 43(8)(2014): 1275-1281

On -Quadratic Stochastic Operators on 2-D Simplex

(-Quadratik Stochastic Pengendali Di Simplex 2-D)

Farrukh Mukhamedov*, Izzat Qaralleh & Wan Nur Fairuz Alwani bt Wan Rozali

Department of Computational & Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box, 141, 25710, Kuantan, Pahang, Malaysia

Diserahkan: 1 Julai 2013/Diterima: 17 Oktober 2013

Abstract

A quadratic stochastic operator (QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. In this paper, we study the –QSO defined on 2D simplex. We first classify –QSO into 2 non-conjugate classes. Further, we investigate the dynamics of these classes of such operators. 

Keywords: Fixed point; quadratic stochastic operator

ABSTRAK

Pengendali stokastik kuadratik (QSO) biasanya digunakan untuk menunjukkan evolusi masa berbeza spesies dalam biologi. Sesetengah pengendali stokastik kuadratik telah dikaji oleh Lotka dan Volterra. Masalah umum dalam teori tak linear pengendali adalah untuk mengkaji tingkah laku pembekal. Masalah ini tidak sepenuhnya siap untuk pengendali stokastik kuadratik yang merupakan pengendali tak linear yang paling mudah. Untuk memahami masalah ini, beberapa kelas QSO telah dikaji. Dalam kertas ini, kami mengkaji – QSO yang ditentukan pada simpleks 2D. Kami mengklasifikasikan – QSO ke dalam kelas bukan konjugat. Seterusnya, kami mengkaji kedinamikan kelas pengusaha terbabit.

Kata kunci: Pengendali stokastik kuadratik; titik tetap

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*Pengarang untuk surat-menyurat; email: farrukh_m@iium.edu.my