On sharp conditions for the global stability of a difference equation satisfying the Yorke condition
Continuing our previous investigations, we give simple sufficient conditions for global stability of the zero solution of the difference equation xn+1 = qxn + fn (xn ,..., xn-k ), n ∈ Z, where nonlinear functions fn 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.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 1, pp 78-90.
Citation Example: Nenya O. I., Tkachenko V. I., Trofimchuk S. I. On sharp conditions for the global stability of a difference equation satisfying the Yorke condition // Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 73–80.