## $$F$$-quadratic stochastic operators.(English. Russian original)Zbl 1167.92023

Math. Notes 83, No. 4, 554-559 (2008); translation from Mat. Zametki 83, No. 4, 606-612 (2008).
Motivated by applications to mathematical genetics, the authors study a special class of quadratic transformations of the unit simplex $$S^m\subset {\mathbb{R}}^{m+1}$$ into itself. Using elementary methods, they prove that for each function from this class and any $$x^{(0)} \in S^m$$ the trajectory $$\{ x^{(n)}\}$$ is exponentially convergent to the fixed point $$(1,0,...,0)$$.

### MSC:

 92D10 Genetics and epigenetics 47N60 Applications of operator theory in chemistry and life sciences 47H40 Random nonlinear operators 47H10 Fixed-point theorems 37N25 Dynamical systems in biology
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### References:

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