Oscillatory and asymptotic behavior of positive periodic solutions of nonlinear discrete model exhibiting the allee effect

Abstract

In this paper we shall consider the discrete nonlinear delay population model with Allee effect x ( n + 1 ) = x ( n ) exp ( a ( n ) + b ( n ) x p ( n - ω ) - c ( n ) x q ( n - ω ) ) , where a( n), b( n) and c( n) are positive sequences of period ω and p and q are positive integers. We will establish some sufficient conditions for the oscillation of all positive solutions about its positive periodic solution x n ∗ and prove that every nonoscillatory solution converges to { x n ∗ } monotonically as n → ∞.