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- Title
Solutions and Properties of Some Degenerate Systems of Difference Equations.
- Authors
Alzahrani, E. O.; El-Dessoky, M. M.; Elsayed, E. M.; Yang Kuang
- 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 xn+1 = ynyn-1/xn (± 1 ± ynyn-1), yn+1 = xnxn-1/yn (± 1 ± xnxn-1), 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.
- Publication
Journal of Computational Analysis & Applications, 2015, Vol 18, Issue 2, p321
- ISSN
1521-1398
- Publication type
Academic Journal