Dynamics of a modified Nicholson-Bailey host-parasitoid model

摘要

In this paper, we study the qualitative behavior of the following modified Nicholson-Bailey host-parasitoid model: x n + 1 = b x n e ? a y n 1 + d x n , y n + 1 = c x n ( 1 ? e ? a y n ) , $$ x_{n+1}=rac{ b x_{n} e^{-ay_{n}}}{1+d x_{n}},qquad y_{n+1}={cx_{n} igl(1-e^{-ay_{n}}igr)}, $$ where a, b, c, d and the initial conditions x 0 $x_{0}$ , y 0 $y_{0}$ are positive real numbers. More precisely, we investigate the boundedness character, existence and uniqueness of a positive equilibrium point, local asymptotic stability and global stability of the unique positive equilibrium point, and the rate of convergence of positive solutions of the system. Some numerical examples are also given to verify our theoretical results.