Global Attractivity and Periodicity Behavior of a Recursive Sequence.

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-1l + . . ., n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. [ABSTRACT FROM AUTHOR]