On sharp conditions for the global stability of a difference equation satisfying the Yorke condition |
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Authors: | O I Nenya V I Tkachenko S I Trofymchuk |
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Institution: | (1) Kyiv National Economic University, Kyiv, Ukraine;(2) Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine;(3) Institute of Mathematics and Physics, University of Talca, Talca, Chile |
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Abstract: | Continuing our previous investigations, we give simple sufficient conditions for the global stability of the zero solution
of the difference equation x
n+1 = qx
n + ƒn(x
n, …, x
n−k), n ∈ ℤ, where the nonlinear functions ƒn satisfy the Yorke condition. For every positive integer k, we represent the interval (0, 1] as the union of (2k + 2)/3] disjoint subintervals, and, for q from each subinterval, we present a global-stability condition in explicit form. The conditions obtained are sharp for the
class of equations satisfying the Yorke condition.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 73–80, January, 2008. |
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Keywords: | |
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