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Dynamics of the rational difference equations
MANAS: Journal of EngineeringDiscrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in
Burak Oğul
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On the System of High Order Rational Difference Equations. [PDF]
Int Sch Res 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 x n+1 = A + (x n/∑i=1 k y n−i), y n+1 = B + (y n/∑i=1 k x n−i), n = 0,1,…, k ∈ {1,2 ...
Zhang Q, Zhang W, Shao Y, Liu J.
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On Some Solvable Systems of Some Rational Difference Equations of Third Order
Mathematics, 2023 Our aim in this paper is to obtain formulas for solutions of rational difference equations such as xn+1=1±xn−1yn/1−yn,yn+1=1±yn−1xn/1−xn, and xn+1=1±xn−1yn−2/1−yn,yn+1=1±yn−1xn−2/1−xn, where the initial conditions x−2, x−1, x0, y−2, y−1, y0 are non-zero ...
Khalil S. Al-Basyouni +1 more
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Dynamics of a Rational System of Difference Equations in the Plane [PDF]
Advances in Difference Equations, 2011 We consider a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In
Franco Daniel +2 more
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More on Three-Dimensional Systems of Rational Difference Equations [PDF]
Discrete Dynamics in Nature and Society, 2011 We are concerned with a kind of three-dimensional system of rational difference equations, given by Kurbanli (2011). A new expression of solution of the system is presented, and the asymptotical behavior is described. At the same time, we also consider a
Liu Keying +3 more
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Solutions Of The Rational Difference Equations
MANAS: Journal of Engineering, 2018 In this paper the solutions of the following difference equation is examined, (1)where the initial conditions are positive real numbers.
D. Şimşek, B. Oğul
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Explicit Solutions and Bifurcations for a System of Rational Difference Equations
Mathematics, 2019 In this paper, we consider the explicit solution of the following system of nonlinear rational difference equations: x n + 1 = x n - 1 / x n - 1 + r , y n + 1 = x n - 1 y n / x n - 1 y n + r , with ...
Bashir Al-Hdaibat +2 more
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On projective systems of rational difference equations [PDF]
SARAJEVO JOURNAL OF MATHEMATICS, 2011 We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin.
Palladino, Frank J.
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On the Solutions of a System of Third-Order Rational Difference Equations
Discrete Dynamics in Nature and Society, 2018 The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2), yn+1=xnxn-2/(±yn-1±xn-2), n=0,1,…, is clarified in which the initial conditions x-2, x-1, x0, y-2, y-1, y0 are considered as arbitrary positive real ...
A. M. Alotaibi +2 more
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Explicit solutions of rational integrable differential-difference equations
Partial Differential Equations in Applied Mathematics, 2022 The rational integrable differential-difference equations are proposed from a different discrete spectral problem. We proved the Liouville integrability of rational integrable differential-difference equations by deriving its bi-Hamiltonian structures ...
Qiulan Zhao, Muhammad Arham Amin
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