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In this paper, we determine the forbidden set and give an explicit formula for the solutions of the difference equation $x_{n + 1} = \frac{a x_{n} x_{n - 1}}{- b x_{n} + c x_{n - 2}}, n \in ℕ_{0}$ where $a$ , $b$ , $c$ are positive real numbers and the initial conditions $x_{- 2}$ , $x_{- 1}$ , $x_{0}$ are real numbers. We show that every admissible solution of that equation converges to zero if either $a < c$ or $a > c$ with $(a - c) / b < 1$ . When $a > c$ with $(a - c) / b > 1$ , we prove that every admissible solution is unbounded. Finally, when $a = c$ , we prove that every admissible solution converges to zero.

Global behavior of solutions to two classes of second-order rational difference equations.

Basu, Sukanya, Merino, Orlando (2009)

Advances in Difference Equations [electronic only]

Global behavior of the difference equation $x_{n + 1} = \frac{a x_{n - 3}}{b + c x_{n - 1} x_{n - 3}}$

Raafat Abo-Zeid (2015)

Archivum Mathematicum

In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation $x_{n + 1} = \frac{a x_{n - 3}}{b + c x_{n - 1} x_{n - 3}}, n = 0, 1, \dots$ where $a, b, c$ are positive real numbers and the initial conditions $x_{- 3}$ , $x_{- 2}$ , $x_{- 1}$ , $x_{0}$ are real numbers.

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Dynamics of a class of higher order difference equations.

Dynamics of a higher-order nonlinear difference equation.

Dynamics of a rational system of difference equations in the plane.

Exact traveling wave solutions for discrete conservation laws.

Existence results for nonlinear fractional difference equation.

Expressions of solutions for a class of differential equations.

Further extending results of some classes of complex difference and functional equations.

Global asymptotic behavior of $y_{n + 1} = (p y_{n} + y_{n - 1}) / (r + q y_{n} + y_{n - 1})$ .

Global asymptotic stability for a fourth-order rational difference equation.

Global asymptotic stability in a class of difference equations.

Global attraction in a rational recursive relation.

Global behavior of a higher-order difference equation.

Global behavior of a higher-order rational difference equation.

Global behavior of a third order rational difference equation

Global behavior of solutions to two classes of second-order rational difference equations.

Global behavior of the difference equation $x_{n + 1} = \frac{a x_{n - 3}}{b + c x_{n - 1} x_{n - 3}}$

Global behavior of the difference equation $x_{n + 1} = (p + x_{n - 1}) / (q x_{n} + x_{n - 1})$ .

Global dynamics of a competitive system of rational difference equations in the plane.

More on a rational recurrence relation.

On a $(2, 2)$ -rational recursive sequence.

Currently displaying 21 – 40 of 82