Results 1 to 10 of about 121,814 (218)
Analytical Solution to a Third-Order Rational Difference Equation [PDF]
The Scientific World Journal, 2023 Inspired by some open conjectures in a rational dynamical system by G. Ladas and Palladino, in this paper, we consider the problem of solving a third-order difference equation. We comment the conjecture by Ladas.
Alvaro H. Salas +2 more
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ON THE STABILITY OF A THIRD ORDER DIFFERENCE EQUATION
Kırklareli Üniversitesi Mühendislik ve Fen Bilimleri Dergisi, 2020 Bu calismada x_(n+1)=x_(n-1) x_(n-2)+A fark denkleminin A pozitif bir reel sayi ve baslangic kosullari pozitif iken denge noktalari incelendi. Ayrica ilgili fark denkleminin lokal asimptotik kararliligi calisildi.
Erkan Taşdemir +1 more
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ON A THIRD ORDER DIFFERENCE EQUATION
Acta Universitatis Apulensis, 2018 Summary: In this paper, the authors solve the difference equation \[ x_{n+1} =\frac{x_nx_{n-2}}{-ax_n + bx_{n-2}}, \quad n = 0, 1, \dots, \] where \(a\) and \(b\) are positive real numbers and the initial values \(x_{-2}, x_{-1}\) and \(x_0\) are real numbers.
R. Abo-Zeid
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Dynamics of a system of rational third-order difference equation [PDF]
, 2012 In this paper, we study the dynamical behavior of positive solution for a system of a rational third-order difference equation xn+1=xn−2B+yn−2yn−1yn,yn+1=yn−2A+xn−2xn−1xn,n=0,1,…, where A,B∈(0,∞), x−2,x−1,x0∈(0,∞); y−2,y−1,y0∈(0,∞).MSC:39A10.
Qianhong Zhang +2 more
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Asymptotic properties of solutions of third order difference equations
Applicable Analysis and Discrete Mathematics, 2020 We consider the difference equation of the form ?(rn?(pn?xn)) = anf (x?(n)) + bn. We present sufficient conditions under which, for a given solution y of the equation ?(rn?(pn?yn)) = 0, there exists a solution x of the nonlinear equation with the asymptotic behavior xn = yn + zn, where z is a sequence convergent to zero.
Janusz Migda +2 more
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Global behavior of a third order difference equation with quadratic term
Tamkang Journal of Mathematics, 2012 In this paper, we solve and study the global behavior of the admissible solutions of the difference equation $$\begin{aligned} x_{n+1}=\frac{x_{n}x_{n-2}}{-ax_{n-1}+bx_{n-2}}, \quad n=0,1,\ldots , \end{aligned}$$ x n + 1 = x n x n - 2 - a x n - 1 + b x n
R. Abo-zeid, H. Kamal
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Oscillatory criteria for Third-Order difference equation with impulses
Journal of Computational and Applied Mathematics, 2009 The authors investigate the oscillation of a mathematical formula for a third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solution of a third-order impulsive difference equation are obtained. Finally, some examples are included to illustrate the results.
Qiaoluan Li +4 more
semanticscholar +2 more sources
Attractivity of two nonlinear third order difference equations
Journal of the Egyptian Mathematical Society, 2013 Consider the difference equations \[ x_{n+1}=\frac{A-Bx_{n-1}}{C+Dx_{n-2}},\;n=0,1,2,\dots,\tag{\(*\)} \] where \(A,B\) are nonnegative, \(D>0\) and \(C\) is a nonzero real number. Also, \(C+Dx_{n-2}\neq 0\) for all \(n\geq 0\). The author investigates the global attractivity, periodic nature, oscillation and boundedness of all admissible solutions of ...
R. Abo-Zeid
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On a Third‐Order System of Difference Equations with Variable Coefficients [PDF]
Abstract and Applied Analysis, 2012 We show that the system of three difference equations , , and , n ∈ ℕ0, where all elements of the sequences , , , n ∈ ℕ0, i ∈ {1,2, 3}, and initial values x−j, y−j, z−j, j ∈ {0,1, 2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when ...
Stevo Stević +3 more
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Dynamical Behavior of a System of Third-Order Rational Difference Equation [PDF]
Discrete Dynamics in Nature and Society, 2015 This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations , , , where , ; , . Some examples are given to demonstrate the effectiveness of the results
Qianhong Zhang +2 more
semanticscholar +4 more sources