关键词: Discrete population model, oscillation, convergence, uniform persistence,
boundedness.

Abstract:

In this paper, authors study the qualitative behavior of solutions of the dis-
crete population model
xn − xn−1 = xn(a + bxn−k − cx
2
n−k),
where a 2 (0, 1), b 2 (−1, 0), c 2 (0,1), and k is a positive integer. They not only
obtain necessary as well as sufficient and necessary conditions for the oscillation of all
eventually positive solutions about the positive equilibrium, but also obtain some sufficient
conditions for the convergence of eventually positive solutions. Furthermore, authors also
show that such model is uniformly persistent, and that all its eventually positive solutions
are bounded.

Key words: Discrete population model, oscillation, convergence, uniform persistence, boundedness.