scholarly journals On Dynamical Behavior of Discrete Time Fuzzy Logistic Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Qianhong Zhang ◽  
Fubiao Lin
Keyword(s):  
Difference Equation ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Fuzzy Numbers ◽  
Dynamical Behavior ◽  
Logistic Equation ◽  
State Variables ◽  
Initial Value ◽  
Numerical Examples ◽  
Logistic Difference Equation

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.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Lili Jia
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
High Order ◽  
Numerical Examples ◽  
Theoretical Results

The purpose of this paper is to give the conditions for the existence and uniqueness of positive solutions and the asymptotic stability of equilibrium points for the following high-order fuzzy difference equation: xn+1=Axn−1xn−2/B+∑i=3kCixn−i n=0,1,2,…, where xn is the sequence of positive fuzzy numbers and the parameters A,B,C3,C4,…,Ck and initial conditions x0,x−1,x−2,x−ii=3,4,…,k are positive fuzzy numbers. Besides, some numerical examples describing the fuzzy difference equation are given to illustrate the theoretical results.

scholarly journals Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huili Ma ◽  
Huifang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ2u(t-1)=f(t,   u(t))+g(t,   u(t)),  t∈Z1,  T, subject to boundary conditions either u(0)-βΔu(0)=0, u(T+1)=αu(η) or Δu(0)=0, u(T+1)=αu(η), where 0<α<1,   β>0,  and   η∈Z2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.

Non Linear Difference Equation of Orlicz Type

2017 ◽  
Vol 14 (1) ◽  
pp. 306-313
Author(s):  
Awad. A Bakery ◽  
Afaf. R. Abou Elmatty
Keyword(s):  
Difference Equation ◽  
Equilibrium Point ◽  
Positive Solution ◽  
Orlicz Function ◽  
Sufficient Conditions ◽  
Linear Difference Equation ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Numerical Examples ◽  
The Difference

We give here the sufficient conditions on the positive solutions of the difference equation xn+1 = α+M((xn−1)/xn), n = 0, 1, …, where M is an Orlicz function, α∈ (0, ∞) with arbitrary positive initials x−1, x0 to be bounded, α-convergent and the equilibrium point to be globally asymptotically stable. Finally we present the condition for which every positive solution converges to a prime two periodic solution. Our results coincide with that known for the cases M(x) = x in Ref. [3] and M(x) = xk, where k ∈ (0, ∞) in Ref. [7]. We have given the solution of open problem proposed in Ref. [7] about the existence of the positive solution which eventually alternates above and below equilibrium and converges to the equilibrium point. Some numerical examples with figures will be given to show our results.

scholarly journals Some Discussions on the Difference Equationxn+1=α+(xn-1m/xnk)

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Awad A. Bakery
Keyword(s):  
Periodic Solution ◽  
Difference Equation ◽  
Equilibrium Point ◽  
Positive Solution ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Numerical Examples ◽  
The Difference

We give in this work the sufficient conditions on the positive solutions of the difference equationxn+1=α+(xn-1m/xnk),  n=0,1,…, whereα,k, andm∈(0,∞)under positive initial conditionsx-1,  x0to be bounded,α-convergent, the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime two-periodic solution. Our results coincide with that known for the casesm=k=1of Amleh et al. (1999) andm=1of Hamza and Morsy (2009). We offer improving conditions in the case ofm=1of Gümüs and Öcalan (2012) and explain our results by some numerical examples with figures.

scholarly journals Dynamical Behavior of a System of Third-Order Rational Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Qianhong Zhang ◽  
Jingzhong Liu ◽  
Zhenguo Luo
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Positive Solution ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Dynamical Behavior ◽  
Third Order ◽  
Rational Difference Equations ◽  
Rational Difference Equation

This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equationsxn+1=A+xn/yn-1yn-2,yn+1=A+yn/xn-1xn-2,n=0,1,…, whereA∈(0,∞),x-i∈(0,∞);y-i∈(0,∞),i=0,1,2. Some examples are given to demonstrate the effectiveness of the results obtained.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Qiuli He ◽  
Chunyan Tao ◽  
Taixiang Sun ◽  
Xinhe Liu ◽  
Dongwei Su
Keyword(s):  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fuzzy Numbers ◽  
Periodic Sequence

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.

Nonlocal problems arising from the birth-jump processes

2018 ◽  
Vol 149 (2) ◽  
pp. 447-469
Author(s):  
M. Delgado ◽  
A. Suárez ◽  
I. B. M. Duarte
Keyword(s):  
Positive Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Solution Method ◽  
Eigenvalue Problems ◽  
Logistic Equation ◽  
Jump Processes ◽  
Nonlocal Problems

In this paper, we prove the existence and uniqueness of a positive solution for a nonlocal logistic equation arising from the birth-jump processes. For this, we establish a sub-super solution method for nonlocal elliptic equations, we perform a study of the eigenvalue problems associated with these equations and we apply these results to the nonlocal logistic equation.

On Chaotic Behavior

1994 ◽  
Vol 5 (4) ◽  
pp. 232-236 ◽  
Author(s):  
Lawrence M Ward ◽  
Robert L West
Keyword(s):  
Difference Equation ◽  
Chaotic Behavior ◽  
Logistic Equation ◽  
Narrow Sense ◽  
Chaotic Sequences ◽  
The World ◽  
Logistic Difference Equation

Neuringer and Voss (1993) described experiments in which humans generated response sequences that approximated features of chaotic sequences generated by iterating the logistic difference equation Although this demonstration is very interesting, we argue that the logistic equation is not a convincing model of their subjects' behavior Further, although any chaotic behavior is in a narrow sense deterministic, there is reason to believe that the prevalence of chaos actually undermines a more globally deterministic view of the world

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