Results 11 to 20 of about 649,859 (305)
Classification of global behavior of a system of rational difference equations
Applied Mathematics Letters, 2018 This paper deals with a system of rational difference equations x n + 1 = a y n + b c y n + d , y n + 1 = a x n + b c x n + d , n = 0 , 1 , 2 , … , where a , b , c , d are real numbers with c ≠ 0 and a d − b c ≠ 0 .
H. Matsunaga, Rina Suzuki
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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.
Christos J Schinas
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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 two systems of rational difference equations of second order, where the initial conditions are arbitrary nonzero real numbers.
E. Elsayed, Kholoud N. Alharbi
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Dynamics of a Rational Difference Equation [PDF]
Advances in Difference Equations, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wan-Tong Li, Lin-Xia Hu, Xiu-Mei Jia
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Global Stability of a Rational Difference Equation [PDF]
Discrete Dynamics in Nature and Society, 2010 We consider the higher‐order nonlinear difference equation xn+1 = (p + qxn−k)/(1 + xn + rxn−k), n = 0, 1, … with the parameters, and the initial conditions x−k, …, x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above‐mentioned equation. In
Guo-Mei Tang, Lin-Xia Hu, Gang Ma
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Unbounded rational systems with nonconstant coefficients
Nonautonomous Dynamical Systems, 2022 We show the existence of unbounded solutions to difference equations of the form {xn+1=c′nxnBnyn,yn+1=bnxn+cnynAn+Cnyn for n=0,1,…,\left\{ {\matrix{{{x_{n + 1}} = {{{{c'}_n}{x_n}} \over {{B_n}{y_n}}},} \hfill \cr {{y_{n + 1}} = {{{b_n}{x_n} + {c_n}
Kudlak Zachary, Vernon R. Patrick
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Qualitative study of a third order rational system of difference equations [PDF]
Mathematica Moravica, 2021 This paper is concerned with the dynamics of positive solutions for a system of rational difference equations of the following form un+1 = au2 n-1 b + gvn-2 , vn+1 = a1v 2 n-1 b1 + g1un-2 , n = 0, 1, . . .
Gümüş Mehmet, Abo-Zeid Raafat
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Applications of rational difference equations to spectral graph theory [PDF]
Journal of difference equations and applications (Print), 2020 We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find a general closed formula and determine the analytical properties of the solutions.
E. Oliveira, V. Trevisan
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, 2021 The main goal of this paper, is to obtain the forms of the solutions of the following nonlinear fifteenth-order difference equations xn+1 = xn−14 ±1± xn−2xn−5xn−8xn−11xn−14 , n = 0, 1, 2, . . . , where the initial conditions x−14, x−13, . . .
A. M. Ahmed +2 more
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Rational Recursion Operators for Integrable Differential–Difference Equations [PDF]
Communications in Mathematical Physics, 2019 In this paper we introduce preHamiltonian pairs of difference operators and study their connections with Nijenhuis operators and the existence of weakly non-local inverse recursion operators for differential-difference equations. We begin with a rigorous setup of the problem in terms of the skew field $Q$ of rational (pseudo--difference) operators over
Carpentier, S, Mikhailov, AV, Wang, JP
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