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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)
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