Abstract
For nonnegative real numbers ,
,
,
,
,
and
such that
and
, the difference equation
,
has a unique positive equilibrium. A proof is given here for the following statements: (1) For every choice of positive parameters
,
,
,
,
,
and
, all solutions to the difference equation
,
converge to the positive equilibrium or to a prime period-two solution. (2) For every choice of positive parameters
,
,
,
,
and
, all solutions to the difference equation
,
converge to the positive equilibrium or to a prime period-two solution.