Báo Cáo Báo cáo hóa học BEHAVIOR OF THE POSITIVE SOLUTIONS OF FUZZY MAX-DIFFERENCE EQUATIONS G STEFANIDOU AN

BEHAVIOR OF THE POSITIVE SOLUTIONS OF FUZZY MAX-DIFFERENCE EQUATIONS G. STEFANIDOU AND G. PAPASCHINOPOULOS Received 15 September 2004

We extend some results obtained in 1998 and 1999 by studying the periodicity of the solutions of the fuzzy difference equations xn+1 = max{A/xn ,A/xnư1 , .,A/xnưk }, xn+1 = max{A0 /xn ,A1 /xnư1 }, where k is a positive integer, A, Ai , i = 0,1, are positive fuzzy numbers, and the initial values xi , i = ưk, ưk + 1, .,0 (resp., i = ư1,0) of the first (resp., second) equation are positive fuzzy numbers.

1. Introduction

Difference equations are often used in the study of linear and nonlinear physical, physiological, and economical problems (for partial review see [3, 6]). This fact leads to the fast promotion of the theory of difference equations which someone can find, for instance, in [1, 7, 9]. More precisely, max-difference equations have increasing interest since max operators have applications in automatic control (see [2, 11, 17