Global and local behavior of a class of \(\xi^{(s)}\)-QSO. (English) Zbl 1412.37050

Summary: 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 has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. This paper investigates the global behavior of an operator taken from \(\xi^{(s)}\)-QSO when the parameter \(a=\frac{1}{2}\). Moreover, we study the local behavior of this operator at each value of \(a\), where \(0< a < 1\).


37E99 Low-dimensional dynamical systems
37N25 Dynamical systems in biology
39B82 Stability, separation, extension, and related topics for functional equations
47H60 Multilinear and polynomial operators
92D25 Population dynamics (general)
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