scholarly journals Periodic Solution for a Max-Type Fuzzy Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Changyou Wang ◽  
Jiahui Li
Keyword(s):  
Periodic Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Software Package ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Equation System ◽  
Mathematical Induction ◽  
Inequality Technique ◽  
Boundedness And Persistence

The paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1=maxA/xn, A/xn−1, xn−2, n=0,1,2,…, where xn is a sequence of positive fuzzy numbers, and the parameter A and the initial conditions x−2, x−1, x0 are also positive fuzzy numbers. Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters. Then, the expression for the periodic solution of the max-type ordinary difference equations is obtained by the iteration, the inequality technique, and the mathematical induction. Moreover, we can obtain the expression for the periodic solution of the max-type fuzzy difference equation. In addition, the boundedness and persistence of solutions for the fuzzy difference equation is proved. Finally, the results of this paper are simulated and verified by using MATLAB 2016 software package.

scholarly journals Asymptotic Behavior of a Second-Order Fuzzy Rational Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Q. Din
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Existence Of Positive Solutions ◽  
Rational Difference Equation ◽  
Boundedness And Persistence ◽  
Theoretical Results

We study the qualitative behavior of the positive solutions of a second-order rational fuzzy difference equation with initial conditions being positive fuzzy numbers, and parameters are positive fuzzy numbers. More precisely, we investigate existence of positive solutions, boundedness and persistence, and stability analysis of a second-order fuzzy rational difference equation. Some numerical examples are given to verify our theoretical results.

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 Analytical Study of the Difference Equation xn+1 = xnxn-6 / xn-5 (±1 – xnxn-6)

2019 ◽  
pp. 1-12
Author(s):  
Abdualrazaq Sanbo ◽  
Elsayed M. Elsayed ◽  
Faris Alzahrani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Analytical Study ◽  
Initial Conditions ◽  
Specific Form ◽  
Positive Real ◽  
Rational Difference Equations ◽  
Special Cases ◽  
The Difference

This paper is devoted to find the form of the solutions of a rational difference equations with arbitrary positive real initial conditions. Specific form of the solutions of two special cases of this equation are given.

scholarly journals Existence of a Period-Two Solution in Linearizable Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
E. J. Janowski ◽  
M. R. S. Kulenović
Keyword(s):  
Difference Equation ◽  
Linear Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Minimal Period ◽  
Real Numbers ◽  
Existence And Nonexistence ◽  
The Difference ◽  
Necessary And Sufficient

Consider the difference equationxn+1=f(xn,…,xn−k),n=0,1,…,wherek∈{1,2,…}and the initial conditions are real numbers. We investigate the existence and nonexistence of the minimal period-two solution of this equation when it can be rewritten as the nonautonomous linear equationxn+l=∑i=1−lkgixn−i,n=0,1,…,wherel,k∈{1,2,…}and the functionsgi:ℝk+l→ℝ. We give some necessary and sufficient conditions for the equation to have a minimal period-two solution whenl=1.

Dynamics of a Higher Order Rational Difference Equation

2011 ◽  
Vol 216 ◽  
pp. 50-55 ◽  
Author(s):  
Yi Yang ◽  
Fei Bao Lv
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Higher Order ◽  
Rational Difference Equation ◽  
The Difference

In this paper, we address the difference equation xn=pxn-s+xn-t/q+xn-t n=0,1,... with positive initial conditions where s, t are distinct nonnegative integers, p, q > 0. Our results not only include some previously known results, but apply to some difference equations that have not been investigated so far.

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.

Existence and Stability of Difference Equation in Imprecise Environment

2018 ◽  
Vol 7 (4) ◽  
pp. 263-271 ◽  
Author(s):  
Sankar Prasad Mondal ◽  
Najeeb Alam Khan ◽  
Dileep Vishwakarma ◽  
Apu Kumar Saha
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Numerical Experiments ◽  
Fuzzy Numbers ◽  
Fuzzy Theory ◽  
Efficient Solutions ◽  
Triangular Fuzzy Numbers ◽  
First Order ◽  
Fuzzy Environment ◽  
Existence And Stability

AbstractIn this paper, first order linear homogeneous difference equation is evaluated in fuzzy environment. Difference equations become more notable when it is studied in conjunction with fuzzy theory. Hence, here amelioration of these equations is demonstrated by three different tactics of incorporating fuzzy numbers.Subsequently, the existence and stability analysis of the attained solutions of fuzzy difference equations (FDEs) are then discussed under different cases of impreciseness. In addition, considering triangular and generalized triangular fuzzy numbers, numerical experiments are illustrated and efficient solutions are depicted, graphically and in tabular form.

On a recursive sequence

Kybernetes ◽  
2007 ◽  
Vol 36 (1) ◽  
pp. 98-115
Author(s):  
Mehdi Dehghan ◽  
Reza Mazrooei‐Sebdani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Open Problem ◽  
Design Methodology ◽  
Initial Conditions ◽  
Open Problems ◽  
Content Type ◽  
Rational Difference Equations ◽  
Global Behaviour ◽  
Recursive Sequence

PurposeThe aim in this paper is to investigate the dynamics of difference equation yn+1=(pyn+yn−k)/(qyn+yn−k), n=0,1,2,… where k∈{1,2,3,…}, the initial conditions y−k, … ,y−1,y0 and the parameters p and q are non‐negative.Design/methodology/approachThe paper studies characteristics such as the character of semicycles, periodicity and the global stability of the above mentioned difference equation.FindingsIn particular, the results solve the open problem introduced by Kulenovic and Ladas in their monograph, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures.Originality/valueThe global behaviour of the solutions of equation yn+1=(pyn+yn−k)/(qyn+yn−k), n=0,1,2,… were investigated providing valuable conclusions on practical data.

scholarly journals On the Dynamics of the Recursive Sequence

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Mehmet Gümüş ◽  
Özkan Öcalan ◽  
Nilüfer B. Felah
Keyword(s):  
Periodic Solution ◽  
Difference Equation ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Recursive Sequence ◽  
Boundedness Character ◽  
The Difference

We investigate the boundedness character, the oscillatory, and the periodic character of positive solutions of the difference equation , where , , and the initial conditions are arbitrary positive numbers. We investigate the boundedness character for . Also, we investigate the existence of a prime two periodic solution for is odd. Moreover, when is even, we prove that there are no prime two periodic solutions of the equation above.

scholarly journals Solution of the Maximum of Difference Equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn}\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}

2020 ◽  
Vol 5 (1) ◽  
pp. 275-282
Author(s):  
Dagistan Simsek ◽  
Burak Ogul ◽  
Fahreddin Abdullayev
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Initial Conditions ◽  
Type System ◽  
Global Behavior ◽  
System Of Difference Equations

AbstractIn the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations, (1)\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}} where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.

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