Results 261 to 270 of about 649,859 (305)

Progress Report on Rational Difference Equations

The Journal of Difference Equations and Applications, 2003
Our aim here is to present a summary of our recent work and a large number of open problems and conjectures on third order rational difference equations of the form with non-negative parameters and non-negative initial conditions.
Grove, E. A., Kulenović, M. R.S., Ladas, G.   +2 more
openaire   +2 more sources

Analytical solution of a rational difference equation

Advanced Studies: Euro-Tbilisi Mathematical Journal, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khaliq, Abdul, Hassan, Sk. Sarif
openaire   +1 more source

Global Dynamical Properties of a System of Quadratic-Rational Difference Equations With Arbitrary Delay

Sarajevo Journal of Mathematics
In this paper, we investigate the global dynamics of the following system of quadratic-higher order difference equations:\begin{equation*}x_{n+1}=A+B\frac{y_{n}}{y_{n-m}^{2}},y_{n+1}=A+B\frac{x_{n}}{x_{n-m}^{2}}\end{equation*}where $A$ and $B$ are ...
E. Taşdemir
semanticscholar   +1 more source

Neimark–Sacker bifurcation of two second-order rational difference equations

Journal of difference equations and applications (Print)
We investigate the Neimark–Sacker bifurcation of the equilibrium of two special cases of the difference Equation \[ x_{n+1}=\frac{\beta x_n x_{n-1}+ \gamma x_{n-1}^2 +\delta x_n}{B x_n x_{n-1}+C x_{n-1}^2 +D x_n} \]xn+1=βxnxn−1+γxn−12+δxnBxnxn−1+Cxn−12 ...
M. Kulenović, C. O’Loughlin, E. Pilav
semanticscholar   +1 more source

Dynamics of a rational difference equation

Applied Mathematics and Computation, 2005
The authors investigate the periodic character, invariant intervals, oscillation and global stability of all positive solutions of the equation \[ {x_{n+1}=\frac{px_{n}+x_{n-k}}{q+x_{n-k}}~\;,~\;\;n=0,1,\dots,}\tag{*} \] where \(p\) and \(q\) and the initial conditions \(x_{-k},\dots,x_{0}\) are nonnegative real numbers.
Li, Wantong, Sun, Hongrui
openaire   +1 more source

On the boundedness of solutions of a class of third-order rational difference equations

Journal of difference equations and applications (Print), 2018
We consider the difference equation with and If we show that for all positive initial conditions the solutions of the difference equations are bounded. If then there exists positive initial conditions such that the solutions are unbounded.
Y. Huang, P. Knopf
semanticscholar   +1 more source

Dynamics of a rational difference equation

Chinese Annals of Mathematics, Series B, 2009
The article deals with some properties of the solutions of the difference equation \[ x_{n+1} = \frac{ax_{n-l}x_{n-k}}{bx_{n-p} + cx_{n-q}}, \qquad n = 0,1,\dots,\tag{1} \] with the initial condition \(x_{-r},x_{-r+1},\dots,x_0\) that are arbitrary positive reals, \(r = \max \;\{l,k,p,q\}\); \(a, b, c\) are positive constants.
Elabbasy, Elmetwally M., Elsayed, Elsayed M.   +1 more
openaire   +2 more sources

Dynamics of the Rational Difference Equation

Information Sciences Letters, 2014
In this article, we study the periodicity, the boundedness and the global stab ility of the positive solutions of the following nonlinear difference ...
M. A. El-Moneam, E. M. E. Zayed
openaire   +1 more source

Dynamics of a rational difference equation

Applied Mathematics and Computation, 2006
Abstract In this note, we investigate the solution of the difference equation x n + 1 = x n - 1 a - x n - 1 x n , n = 0 , 1 , 2 , … , where x - 1 , x 0 ∈ R and a > 0. Moreover, we discuss the stability properties and semi-cycle behavior of this solution.
openaire   +1 more source

Solution of rational difference equation

2019
Summary: The behavior of the solutions of the following system of difference equations is examined, \[ x_{n+1}=\frac{x_{n-27}}{1+x_{n-3}x_{n-7}x_{n-11}x_{n-15}x_{n-19}x_{n-23}} \] where the initial conditions are positive real numbers. The initial conditions of the equation are arbitrary positive real numbers.
Simşek D., Ogul B., Imashkyzy M.
openaire   +2 more sources