Dynamic Behavior of a Fractional-Type Fuzzy Difference System

In this paper, our aim is to study the following fuzzy system: x(n +1) = Ax(n-1)x(n-2) + Bx(n-3)/D+Cx(n-4), n = 0, 1, 2, ..., where fxng is a sequence of positive fuzzy numbers and the initial conditions x(-4), x(-3), x(-2) , x(-1,) x(0) and the parameters A, B, C, D are positive fuzzy numbers. Firstly, the existence and uniqueness of positive fuzzy solutions of the fuzzy system are proved. Secondly, the dynamic behavior of the equilibrium points for the fuzzy system are studied by means of the fuzzy sets theory, linearization method and mathematical induction. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, and the numerical results not only show the dynamic behavior of the solutions for the fuzzy system, but also verify the effectiveness of the proposed results.