Periodicity of the Positive Solutions of a Fuzzy Max-Difference Equation

Abstract

We investigate the periodic nature of the positive solutions of the fuzzy max-difference equationxn+1=maxAn/xn-m,xn-k,n=0,1,…, wherek,m∈{1,2,…},Anis a periodic sequence of fuzzy numbers, andx-d,x-d+1,…,x0are positive fuzzy numbers withd=m,k. We show that every positive solution of this equation is eventually periodic with periodk+1.

Dynamic Behaviors of a Class of High-Order Fuzzy Difference Equations

“…e following lemmas are applied to study the existence and uniqueness of a positive solution of the fuzzy difference equation (8).…”

“…Hence, it is known that (L n,α , R n,α ) satisfies the family of system (18). e following corresponding ordinary parametric systems to study the asymptotic behavior of equation (8) are constructed:…”

“…Numerical examples are given in this section to confirm the results of the previous sections and to support the theoretical discussion. e example gives the asymptotic behavior of the solution of the fuzzy difference system (8). e following fuzzy difference equation is considered.…”

“…, y 0 are the positive numbers and p and q are the positive integers. In 2014, He et al [8] studied the periodicity of the positive solutions for the following fuzzy max-difference equation:…”

Dynamics of the fuzzy difference equation z n = max { 1 z n − m , α n z n − r }

“…, z −1 with d = max{k, m} are positive fuzzy numbers. In 2014, He et al [3] investigated the periodicity of the positive solutions of the fuzzy max-difference equation…”