Dynamic behavior of a seven-order fuzzy difference equation

In this paper, we explore the qualitative features of a seven-order fuzzy difference equation xn+1 = Axn-1 B+Cxp n-2xq n-4 xrn-6 , n = 0, 1, 2,center dot center dot center dot , here the parameters A, B, C is an element of R+f , p, q, r is an element of R+ and the initial values x-6,center dot center dot center dot ,x-1, x0 is an element of R+f. Utilizing the fuzzy sets theory, linearization method, mathematical induction and inequality technique, we obtain some sufficient condition on the qualitative features including the boundedness of the positive solution of the equation and the stability and instability of the equilibrium point of the equation. Moreover, two simulation examples are presented to verify the ef-fectiveness of our proposed results.