On sharp conditions for the global stability of a difference equation satisfying the Yorke condition

  • O. I. Nenya
  • V. I. Tkachenko
  • S. I. Trofimchuk


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.
How to Cite
Nenya, O. I., V. I. Tkachenko, and S. I. Trofimchuk. “On Sharp Conditions for the Global Stability of a Difference Equation Satisfying the Yorke Condition”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 1, Jan. 2008, pp. 73–80, https://umj.imath.kiev.ua/index.php/umj/article/view/3138.
Research articles