Stability of a Class of Nonlinear Difference Equations

AbstractIn this paper using KAM theory we investigate the stability nature of the zero equilibrium of the system of two nonlinear difference equations [equation] whereai,bi,ci,i=1,2, are real constants andf: R→R is aC∞function

On a modification of a discrete epidemic model

AbstractIn this paper under some conditions on the constants A,B∈(0,∞) we study the existence of positive solutions, the existence of a unique nonnegative equilibrium and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations xn+1=(1−yn−yn−1)(1−e−Ayn),yn+1=(1−xn−xn−1)(1−e−Bxn) where A,B∈(0,∞) and the initial values x−1,x0,y−1,y0 are positive numbers which satisfy the relations x0+x−1<1,y0+y−1<1,1−y0>(1−x0−x−1)(1−e−Bx0),1−x0>(1−y0−y−1)(1−e−Ay0)

Behavior of the positive solutions of fuzzy max-difference equations

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/xn−1,…,A/xn−k}, xn+1=max{A0/xn,A1/xn−1}, where k is a positive integer, A, Ai, i=0,1, are positive fuzzy numbers, and the initial values xi, i=−k,−k+1,…,0 (resp., i=−1,0) of the first (resp., second) equation are positive fuzzy numbers

Asymptotic behavior of the solutions of a class of rational difference equations

Abstract In this paper we study the asymptotic behavior of the positive solutions of certain rational difference equations

On the system of two nonlinear difference equations x

We study the oscillatory behavior, the periodicity and the asymptotic behavior of the positive solutions of the system of two nonlinear difference equations xn+1=A+xn−1/yn and yn+1=A+yn−1/xn, where A is a positive constant, and n=0,1,…