Global attractivity for discrete models of nonautonomous logistic equations

Consider the following discrete model of a nonautonomous logistic equation: {N(n+1)=N(n)exp{c(n)−∑j=0mbj(n)N(n−j)},n≥0,N(0)=N0>0andN(−j)=N−j≥0,1≤j≤m, where c(n)c(n) and bj(n),0≤j≤m,n≥0 are bounded and c(n)>0,b0(n)>0,bj(n)≥0,1≤j≤m,n≥0. In this paper, using some kind of iterative method to the above equation, we establish sufficient conditions that ensure the global attractivity for solutions. The result is an extension of the former work [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2004) 560–580] to the nonautonomous case.