On Dynamical Behavior of Discrete Time Fuzzy Logistic Equation

Abstract

The aim of this paper is to investigate the dynamical behavior of the following model which describes the logistic difference equation taking into account the subjectivity in the state variables and in the parameters. xn+1=Axn(1~-xn), n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers. A,1~ and the initial value x0 are positive fuzzy numbers. The existence and uniqueness of the positive solution and global asymptotic behavior of all positive solution of the fuzzy logistic difference equation are obtained. Moreover, some numerical examples are presented to show the effectiveness of results obtained.

Solution and Interpretation of Neutrosophic Homogeneous Difference Equation

“…National income determination models with fuzzy stability analysis in a discrete system are elaborately discussed by Sarkar et al [32]. The fuzzy discrete logistic equation is taken and stability situations are found in the literature [33]. Zhang et al [34] show the asymptotic performance of a discrete time fuzzy single species population model.…”

Asymptotic Behavior of Discrete Time Fuzzy Single Species Model

“…The fuzzy number space {( ( ), ( ))} becomes a convex cone 1 which could be embedded isomorphically and isometrically into a Banach space. [26] Definition . Let = ( ( ), ( )), V = (V( ), V( )) ∈ 1 , 0 ≤ ≤ 1, and arbitrary ∈ .…”

“…In recent decades, researchers have an increasing interest in studying fuzzy difference equation. Some results on fuzzy difference equations have been reported (see, for example, [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]). Barros,Bassanezi,and Tonelli [32] have investigated the dynamical behavior of population model with fuzzy uncertainty.…”

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

“…x 0 are the positive fuzzy numbers. Besides, some interesting results can be found in [13][14][15][16][17][18] and the references therein. Based on the above valuable theoretical results, this paper studies the following high-order fuzzy difference equation:…”