On second-order fuzzy discrete population model

Abstract

This work is concerned with dynamical behavior of a second-order fuzzy discrete population model: x n = A x n − 1 1 + x n − 1 + B x n − 2 , n = 1 , 2 , … , {x}_{n}=\frac{A{x}_{n-1}}{1+{x}_{n-1}+B{x}_{n-2}},\hspace{1em}n=1,2,\ldots , where A , B A,B are positive fuzzy numbers. x n {x}_{n} is a positive fuzzy number and represents the population size at the observation instant n. According to a generalization of division ( g g -division) of fuzzy number, we study the dynamical behaviors including boundedness, global asymptotical stability, and persistence of positive fuzzy solution. Finally, two examples are given to demonstrate the effectiveness of the results obtained.