Results 11 to 20 of about 35,763 (256)
On the Solutions of Three-Dimensional Rational Difference Equation Systems
Journal of Mathematics, 2021 In this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system:xn+1=ynzn−1/yn±xn−2,yn+1=znxn−1/zn±yn−2, and zn+1=xnyn−
H. S. Alayachi +2 more
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On Stability Analysis of Higher-Order Rational Difference Equation
Discrete Dynamics in Nature and Society, 2020 In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0 ...
Abdul Khaliq +3 more
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On a Conjecture for a Higher-Order Rational Difference Equation
Advances in Difference Equations, 2009 This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation xn=(∏j=1m(xn−kj+1)+∏j=1m(xn−kj−1))/(∏j=1m(xn−kj+1)−∏j=1m(xn− ...
Maoxin Liao, Xianhua Tang, Changjin Xu
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On a Rational $(P+1)$th Order Difference Equation with Quadratic Term
Universal Journal of Mathematics and Applications, 2022 In this paper, we derive the forbidden set and determine the solutions of the difference equation that contains a quadratic term \begin{equation*} x_{n+1}=\frac{x_{n}x_{n-p}}{ax_{n-(p-1)}+bx_{n-p}},\quad n\in\mathbb{N}_0, \end{equation*} where the ...
R Abo-zeıd, Messaoud Berkal
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A rational difference equation
Computers & Mathematics with Applications, 2001 The authors investigate the nonlinear rational difference equation \[ x_{n+1}= (\alpha x_n+ \beta x_{n-1})/(A+x_{n-1}),\;n=0,1,2,\dots, \tag{*} \] where the parameters \(\alpha,\beta\) and \(A\) and the initial conditions \(x_{-1}\) and \(x_0\) are nonnegative real numbers.
Kulenović, M. R.S. +2 more
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On the System of High Order Rational Difference Equations [PDF]
International Scholarly Research Notices, 2014 This paper is concerned with the boundedness, persistence, and global asymptotic behavior of positive solution for a system of two rational difference equations xn+1=A+(xn/∑i=1kyn-i), yn+1=B+(yn/∑i=1kxn-i), n=0,1,…,k∈{1,2,…}, where A,B∈0,∞, x-i∈0,∞, and y-i∈0,∞, i=0,1,2,…,k.
Zhang, Qianhong +3 more
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Qualitative Behavior of Rational Difference Equation of Big Order
Discrete Dynamics in Nature and Society, 2013 We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequence xn+1=axn-l+bxn-x/c+dxn-lxn-k, n=0,1,…, where the parameters a, b, c, and d are positive real numbers, and the initial conditions x-t,x-t+1,…,x-1 ...
M. M. El-Dessoky
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Dynamics and Bifurcation of a Second Order Quadratic Rational Difference Equation
Journal of Mathematical Sciences and Modelling, 2020 In this paper, we study the dynamics and bifurcation of $$ x_{n+1} = \frac{\alpha+ \beta {x^2}_{n-1}}{A+B {x_n}+C{x^2}_{n-1}}, \ n=0,\ 1, \ 2, \ ... $$ with positive parameters $\alpha,\ \beta, \ A, \ B, \ C, $ and non-negative initial conditions.
Mohammad Saleh, Shahd Herzallah
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Известия Иркутского государственного университета: Серия "Математика", 2022 Generating functions and difference equations are a powerful tool for studying problems of enumerative combinatorial analysis. In the one-dimensional case, the space of solutions of the difference equation is finite-dimensional.
E.K. Leinartas, T. I. Yakovleva
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On the solutions of systems of rational difference equations
Mathematical and Computer Modelling, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nouressadat Touafek, E. M. Elsayed
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