关键词: Population model, oscillation, convergence, permanence

Abstract:

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation model
xn+1 = axn +bxn(1 + xpn−k)c, n = 0, 1, · · · ,
where 0 < a < 1 < a + b, p, c 2 (0,1) and k is a nonnegative integer, is investigated.Some necessary and sufficient as well as sufficient conditions for all solutions of the modelto oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions are derived. Furthermore,the permanence of every positive solution of the model is also showed. Many known results are improved and extended and some new results are obtained for G. Ladas’ open problems.

Key words: Population model, oscillation, convergence, permanence