Results 11 to 20 of about 274,060 (275)
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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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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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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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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Global Behavior of a System of Second-Order Rational Difference Equations
Communications in Advanced Mathematical Sciences, 2021 In this paper, we consider the following system of rational difference equationsxn+1=a+xnb+cyn+dxn−1, yn+1=α+ynβ+γxn+ηyn−1, n=0,1,2,...xn+1=a+xnb+cyn+dxn−1, yn+1=α+ynβ+γxn+ηyn−1, n=0,1,2,...where a,b,c,d,α,β,γ,η∈(0,∞)a,b,c,d,α,β,γ,η∈(0,∞) and the ...
Phong Mai Nam
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Existence of meromorphic solutions of first order difference equations [PDF]
, 2018 It is shown that if It is shown that if \begin{equation}\label{abstract_eq} f(z+1)^n=R(z,f),\tag{\dag} \end{equation} where $R(z,f)$ is rational in $f$ with meromorphic coefficients and $\deg_f(R(z,f))=n$, has an admissible meromorphic solution ...
Korhonen, Risto, Zhang, Yueyang
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Discrete Miura Opers and Solutions of the Bethe Ansatz Equations [PDF]
, 2004 Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra come in families called the populations. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra. The proof is based on the
Alexander Varchenko +8 more
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On a Competitive System of Rational Difference Equations
Universal Journal of Mathematics and Applications, 2019 This paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form $$ x_{n+1}^{(1)}=\frac{
Mehmet Gümüş
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Bifurcation and Chaos Control of a System of Rational Difference Equations
Results in Nonlinear Analysis, 2021 We study a system of rational dierence equations in this article. For equilibrium points, we present the stability conditions. In addition, we show that the system encounters period-doubling bifurcation at the trivial equilibrium point O and Neimark ...
Rizwan Ahmed, Shehraz Akhtar, Muzammil Mukhtar, Faiza Anwar
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Global Behavior of Solutions to Two Classes of Second Order Rational Difference Equations [PDF]
, 2008 For nonnegative real numbers $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$ such that $B+C>0$ and $\alpha+\beta+\gamma >0$, the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma x_{n-1}}{A+B x_{n}+C x_{n-1 ...
Basu, Sukanya, Merino, Orlando
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