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On the rate of convergence to the neutral attractor of a family of one-dimensional maps

T. Nowicki, M. Sviridenko, G. Świrszcz, S. Winograd (2009)

Fundamenta Mathematicae

For a family of maps f d ( p ) = 1 - ( 1 - p / d ) d , d ∈ [2,∞], p ∈ [0,1]. we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.

On the rational recursive sequence x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k

E. M. E. Zayed, M. A. El-Moneam (2010)

Mathematica Bohemica

The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k , n = 0 , 1 , 2 , where the coefficients α i , β i ( 0 , ) for i = 0 , 1 , 2 , and l , k are positive integers. The initial conditions x - k , , x - l , , x - 1 , x 0 are arbitrary positive real numbers such that l < k . Some numerical experiments are presented.

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