A GLOBAL BEHAVIOR OF THE POSITIVE SOLUTIONS OF xn+1=βxn+ xn-2 ⁄ A+Bxn + xn-2

Title & Authors
A GLOBAL BEHAVIOR OF THE POSITIVE SOLUTIONS OF xn+1=βxn+ xn-2 ⁄ A+Bxn + xn-2
Park, Jong-An;

Abstract
In this paper we prove that every positive solution of the third order rational difference equation $\small{x_{n+1}\;=\;\frac{{\beta}x_n\;+\;x_{n-2}}{A\;+\;Bx_n\;+\;x_{n-2}}}$ converges to the positive equilibrium point $\small{\bar{x}\;=\;\frac{{\beta}\;+\;1\;-\;A}{B\;+\;1}}$, where $\small{0\;}$<$\small{\;{\beta}\;{\leq}\;B}$, $\small{1\;}$<$\small{\;A\;}$<$\small{\;{\beta}\;+\;1}$
Keywords
difference equations;equilibrium point;
Language
English
Cited by
1.
RATIONAL DIFFERENCE EQUATIONS WITH POSITIVE EQUILIBRIUM POINT,;

대한수학회보, 2010. vol.47. 3, pp.645-651
1.
RATIONAL DIFFERENCE EQUATIONS WITH POSITIVE EQUILIBRIUM POINT, Bulletin of the Korean Mathematical Society, 2010, 47, 3, 645
2.
On the Difference equation xn+1=axn−l+bxn−k+cxn−sdxn−s−e, Mathematical Methods in the Applied Sciences, 2016
3.
Evaluation of modeling techniques for a type III hydrogen pressure vessel (70 MPa) made of an aluminum liner and a thick carbon/epoxy composite for fuel cell vehicles, International Journal of Hydrogen Energy, 2012, 37, 3, 2353
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