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

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)