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

7 Citations (Scopus)

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

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System of Difference Equations
Difference equations
Rational Difference Equation
Age Structure
Population Growth
Qualitative Properties
Difference equation
Initial conditions
Interaction
Modeling

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics

Cite this

Solutions and properties of some degenerate systems of difference equations. / Alzahrani, E. O.; El-Dessoky, M. M.; Elsayed, E. M.; Kuang, Yang.

In: Journal of Computational Analysis and Applications, Vol. 18, No. 2, 01.02.2015, p. 321-333.

Research output: Contribution to journalArticle

Alzahrani, E. O. ; El-Dessoky, M. M. ; Elsayed, E. M. ; Kuang, Yang. / Solutions and properties of some degenerate systems of difference equations. In: Journal of Computational Analysis and Applications. 2015 ; Vol. 18, No. 2. pp. 321-333.
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