Behavior of the positive solutions of the generalized Beddington-Holt equation. (English) Zbl 1039.39005

Stević, Stevo

Panam. Math. J. 10, No. 4, 77-85 (2000).

Summary: We consider the asymptotic behaviour of the positive solutions of the generalized Beddington-Holt equation \[ x_{n+k} =ax_{n+k-1} +\sum^{k-1}_{i=0} \frac {b_ix_{n+i-1}} {1+c_ix_{n+i-1} +d_ix_{n+i}},\;n=1,2,3, \dots \] near the zero equilibrium. When \(k=1\), we also consider the asymptotic behaviour of the positive solutions of the generalized Beddington-Holt equation near the positive equilibrium.

MSC:

39A11	Stability of difference equations (MSC2000)
39A20	Multiplicative and other generalized difference equations
92D25	Population dynamics (general)

Keywords:

population dynamics; asymptotic behaviour; positive solutions; generalized Beddington-Holt equation; positive equilibrium