Asymptotic Behavior of Discrete Time Fuzzy Single Species Model

Abstract

This work is concerned with the qualitative behavior of discrete time single species model with fuzzy environment xn+1=xnexp⁡A-Bxn,  n=0,1,2,…, where xn denotes the number of individuals of generation n, A is the intrinsic growth rate, and B is interpreted as the carrying capacity of the surrounding environment. xn is a sequence of positive fuzzy number. A,B and the initial value x0 are positive fuzzy numbers. Applying difference of Hukuhara (H-difference), the existence, uniqueness of the positive solution, and global asymptotic behavior of all positive solution with the model are obtained. Moreover a numerical example is presented to show the effectiveness of theoretic results obtained.