On a second order rational difference equation. (English) Zbl 1277.39021
The difference equation \(x_{n+1}= f(x_n, x_{n-1})\), where \(f\) is a rational function with homogeneous polynomials of degree 4 with positive coefficients in numerator and denominator, is investigated with respect to local resp. global asymptotic stability, permanence and periodicity.
Reviewer: Lothar Berg (Rostock)
MSC:
39A20 | Multiplicative and other generalized difference equations |
39A22 | Growth, boundedness, comparison of solutions to difference equations |
39A30 | Stability theory for difference equations |
39A23 | Periodic solutions of difference equations |