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 language | English (US) |
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Pages (from-to) | 321-333 |
Number of pages | 13 |
Journal | Journal of Computational Analysis and Applications |
Volume | 18 |
Issue number | 2 |
State | Published - Feb 2015 |
Keywords
- Difference equations
- Periodic solution
- Recursive sequences
- Stability
- System of difference equations
ASJC Scopus subject areas
- Computational Mathematics