This paper is concerned with the following high-order nonlinear fuzzy difference system $ {x_{n + 1}} = \frac{{A{\kern 1pt} {x_{n - m}}}}{{B + C{\kern 1pt} \prod\limits_{i = 0}^m {{x_{n - i}}} }}, {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} n = 0, 1, 2, \cdots , $ where $ {x_n} $ is a sequence of positive fuzzy numbers, the parameters and the initial conditions $ {x_{ - m}}, \;{x_{ - m + 1}}, \; \cdots , {x_0} $ are positive fuzzy numbers, $ m $ is non-negative integer. More accurately, our main purpose is to study the existence and uniqueness of the positive solutions, the boundedness of the positive solutions, the instability, local asymptotic stability and global asymptotic stability of the equilibrium points for the above equation by using the iteration method, the inequality skills, the mathematical induction, and the monotone boundedness theorem. Moreover, some numerical examples to the difference system are given to verify our theoretical results.

Dynamics of a high-order nonlinear fuzzy difference equation

In recent years, many researchers have tended to use difference equations in mathematical models to explain the problems in different sciences since they have a lot of features such as they enable the scientists to introduce the predictions of their study and it gives more accurate results. In addition, there are various types of nonlinear difference equations that can be studied; one of the most commonly used is rational nonlinear difference equations. However, the research studies in the area of difference equations have two directions: first one is the analysis of the behavior of solutions.'erefore, there are a huge number of articles published to investigate the stability of the equilibrium points and the existence of the periodic solutions for the nonlinear difference equations (see, for example, [1–5]). 'e second direction is to obtain the expressions of the solution if it is possible since there is no explicit and enoughmethods to find the solution of nonlinear difference equations (see, for example, [6–11]). Saleh and Farhat [12] investigated the stability properties and the period two solutions of all nonnegative solutions of the difference equation:

/pdf/dynamics-and-solutions-expressions-of-a-higher-order-24w7m97hjn.pdf

Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

In this paper, we will investigate some qualitative behavior of solutions of the following fourth order difference equation $ n = 0, 1, ..., $ where the initial conditions and$ x_{0}\ $are arbitrary real numbers and the values $ a, \ b, \ c\ $and$ \;d $ are defined as positive real numbers.

Qualitative analysis of a fourth order difference equation

In this work, we aim to study some qualitative properties of higher order nonlinear difference equations. Specifically, we investigate local as well as global stability and boundedness of solutions of this equation. In addition, we will provide solutions to a number of special cases of the studied equation. Also, we present many numerical examples that support the results obtained. The importance of the results lies in completing the results in the literature, which aims to develop the theoretical side of the qualitative theory of difference equations. 

https://www.mdpi.com/2073-8994/14/4/641/pdf?version=1648008921

The Behavior and Structures of Solution of Fifth-Order Rational Recursive Sequence

In this paper, we explore local stability, attractor, periodicity character, and boundedness solutions of the second-order nonlinear difference equation. Finally, obtained results are verified numerically.

/pdf/global-dynamics-boundedness-and-semicycle-analysis-of-a-24zizf0ly7.pdf

Global Dynamics, Boundedness, and Semicycle Analysis of a Difference Equation

In this paper, we study the behavior of the difference equation $x_{n+1}=ax_{n}+\dfrac{bx_{n}x_{n-1}}{cx_{n-1}+dx_{n-2}},~n=0,1,\ldots,$ where the initial conditions $x_{-2},\ x_{-1},\ x_{0}$ are arbitrary positive real numbers and $a,b,c,d$ are positive constants. Also, we give the solution of some special cases of this equation.

Dynamical behavior and solution of nonlinear difference equation via fibonacci sequence

In this article, analysis and investigation have been conducted on the periodic nature as well as the type of the solutions of the subsequent schemes of rational difference equations
with a nonzero real numbers initial conditions.

/pdf/solutions-of-some-difference-equations-systems-and-1remzb0wg8.pdf

Solutions of Some Difference Equations Systems and Periodicity

Abstract This paper proposes a finite difference scheme with a three-level time and a five-point stencil in space to solve an initial boundary value problem for the MRLW equation. The scheme is shown to be marginally stable and convergent with a fourth-order convergence in the space direction and a second-order convergence in the time variable direction with regard to the maximum norm. The conservation properties of the proposed scheme are assessed using the three motion invariants for mass, momentum, and energy. To validate the theoretical results, numerical experiments are given for both single and interaction of two and three solitary waves. 

/pdf/solitary-wave-solutions-of-the-mrlw-equation-using-a-spatial-brbm4o7z.pdf

N. H. Alotaibi

Papers

Dynamical behavior and solution of nonlinear difference equation via fibonacci sequence

Solutions of Some Difference Equations Systems and Periodicity

Solitary wave solutions of the MRLW equation using a spatial five-point stencil of finite difference approximation