Solutions and properties of some degenerate systems of difference equations

E. O. Alzahrani, M. M. El-Dessoky, E. M. Elsayed, Yang Kuang

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

This paper is devoted to obtain the form of the solution and the qualitative properties of the following systems of a rational difference equations of order two (Formula Presented), with positive initial conditions x−1, x0, y−1 and y0 are nonzero real numbers. If we let un = xnxn−1 and vn = ynyn−1, then these systems can be viewed as special cases of the system of the form un+1 = f (vn), vn+1 = g(un). This system has applications in modeling population growth with age structure or the dynamics of plant-herbivore interaction. Let wn = u2n, we have wn+1 = f (g(wn)) ≡ h(wn). At a nonzero steady state w of the last difference equation, we have |h′)| = |f′ (g(w))g′ (w)| = 1, indicating that the system is degenerate at this steady state.

Original languageEnglish (US)
Pages (from-to)321-333
Number of pages13
JournalJournal of Computational Analysis and Applications
Volume18
Issue number2
StatePublished - Feb 1 2015

Keywords

  • Difference equations
  • Periodic solution
  • Recursive sequences
  • Stability
  • System of difference equations

ASJC Scopus subject areas

  • Computational Mathematics

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