Global behavior of a higher-order difference equation (Q980813)

Summary: This paper is concerned with the global behavior of higher-order difference equation of the form \(y_{n+1}=(y_n\exp(\beta(1-2\sum^k_{i=0} a_iy_{n-i})))/(1-y_n+y_n\exp(\beta(1-2\sum^k_{i=0}a_iy_{n-i})))\), \(n=0,1,2,\dots y_{-k},y_{-k+1},\dots,y_0\in (0,1)\). Under some certain assumptions, it is proved that the positive equilibrium is globally asymptotical stable.