Results 41 to 50 of about 1,841,091 (232)
MathematicsIn this paper, we investigate the behavior of solutions to a nonlinear system of rational difference equations of order two, defined by xn+1=xnyn−1yn(a+bxnyn−1),yn+1=ynzn−1zn(c+dynzn−1),zn+1=znxn−1xn(e+fznxn−1), where n denotes a nonzero integer; the ...
Messaoud Berkal +4 more
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$q$-analogue of modified KP hierarchy and its quasi-classical limit
, 2005 A $q$-analogue of the tau function of the modified KP hierarchy is defined by a change of independent variables. This tau function satisfies a system of bilinear $q$-difference equations.
A. Mironov +19 more
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On explicit periodic solutions in three-dimensional difference systems
AIMS MathematicsThis paper focuses on the existence and analytical formulation of closed-form solutions for a three-dimensional system of nonlinear difference equations.
Ahmed Ghezal, Najmeddine Attia
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Parameter interval of positive solutions for a system of fractional difference equation
Advances in Difference Equations, 2020 This paper deals with a typical system of Caputo fractional difference equations. Using the Guo–Krasnosel’skii fixed point theorem, we find a parameter interval for which at least one positive solution of the system exists.
Kazem Ghanbari, Tahereh Haghi
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General solution to subclasses of a two-dimensional class of systems of difference equations
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We show practical solvability of the following two-dimensional systems of difference equations $$x_{n+1}=\frac{u_{n-2}v_{n-3}+a}{u_{n-2}+v_{n-3}},\quad y_{n+1}=\frac{w_{n-2}s_{n-3}+a}{w_{n-2}+s_{n-3}},\quad n\in\mathbb{N}_0,$$ where $u_n$, $v_n,$ $w_n ...
Stevo Stevic
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On the solutions of some systems of rational difference equations
AIMS MathematicsIn this paper, we considered some systems of rational difference equations of higher order as follows$ \begin{eqnarray*} u_{n+1} & = &\frac{v_{n-6}}{1\pm v_{n}u_{n-1}v_{n-2}u_{n-3}v_{n-4}u_{n-5}v_{n-6}}, \\ v_{n+1} & = &\frac{u_{n-6}}{1 ...
M. T. Alharthi
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Eigenvalue Characterization of a System of Difference Equations [PDF]
Nonlinear Oscillations, 2004 We consider the system of difference equations $$u_i (k) = \lambda \mathop \sum \limits_{\ell = 0}^N g_i (k,\ell )P_i (\ell ,u_1 (\ell ),u_2 (\ell ),...,u_n (\ell )), k \in \{ 0,1,...,T\} , 1 \leqslant i \leqslant n,$$ where λ > 0 and T ≥ N ≥ 0. Our aim is to determine the values of λ for which the above system has a constant-sign solution.
Agarwal, R.P. +2 more
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Invariants for Difference Equations and Systems of Difference Equations of Rational Form
Journal of Mathematical Analysis and Applications, 1997 The author consideres the system of difference equations \[ x_{n+1} = \frac{a_n y_n + A}{x_{n-1}}, \qquad y_{n+1} = \frac{b_n x_n + A}{y_{n-1}}, n = 0, 1,\dots\tag{1} \] where the coefficients \(\{a_n\}\) and \(\{b_n\}\) are periodic sequences of positive numbers of period 2 and \(A\) is a positive constant. Some invariants for system (1) are presented.
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Perturbations of Nonlinear Systems of Difference Equations
Journal of Mathematical Analysis and Applications, 1996 Sufficient conditions in order to ensure that the perturbed equation \[ y(n+1)= f(n,y(n))+ g(n,y(n)) \] inherits its stability from the equation \[ x(n+1)= f(n,x(n)), \] are given.
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The expressions and behavior of solutions for nonlinear systems of rational difference equations
Journal of Innovative Applied Mathematics and Computational Sciences, 2022 In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,
Kholoud N. Alharbi, E. M. Elsayed
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