References
-
R. Abu-Saris, C. Cinar, I. Yalcinkaya, On the asymptotic stability of
$x_{n+1}$ =$\frac{ , Computers & Mathematics with Applications 56 (2008), 1172-1175. https://doi.org/10.1016/j.camwa.2008.02.028$x_nx_{n-k}$ }{$x_n$ +$x_{n-k}$ }$ -
A. Andruch-Sobilo, M. Migda, On the rational recursive sequence
$x_{n+1}$ =$\frac{ , Tatra Mountain Mathematical Publications 43 (2009), 1-9. https://doi.org/10.2478/v10127-009-0020-y$ax_{n-1}$ }{b+$cx+nx_{n-1}$ }$ - I. Bajo, E. Liz, Global behaviour of a second-order nonlinear difference equation, J. Differ. Equations Appl. 17 (2011), 1471-1486. https://doi.org/10.1080/10236191003639475
- E. Camouzis and G. Ladas. Dynamics of Third-order Rational Difference Equations with Open Problems and Conjectures, Volume 5 of Advances in Discrete Mathematics and Applications, Chapman & Hall/CRC, Boca Raton, FL, 2008.
-
C. Cinar, On the positive solutions of the difference equation
$x_{n+1}$ =$\frac{ , Applied Mathematics and Computation 150 (2004), 21-24. https://doi.org/10.1016/S0096-3003(03)00194-2$x_{n-1}$ }{1+$x_nx_{n-1}$ }$ - M. Dehghan, N. Rastegar, Stability and periodic character of a third order difference equation, Mathematical and Computer Modelling 54 (2011), 2560-2564. https://doi.org/10.1016/j.mcm.2011.06.025
- E.M. Elabbasy, S.M. Eleissawy, Qualitative properties for a higher order rational difference equation, Fasciculi Mathematici (2013), 33-50.
- H. El-Metwally, E.M. Elsayed, Qualitative study of solutions of some difference equations, Abstract and Applied Analysis 2012 (2012), Article ID 248291, 16 pages.
-
H.M. El-Owaidy, A.M. Ahmet, A.M. Youssef, On the dynamics of the recursive sequence
$x_{n+1}$ =$\frac{ , Applied Mathematics Letters 18 (2005), 1013-1018. https://doi.org/10.1016/j.aml.2003.09.014${\alpha}x_{n-1}$ }{${\beta}+{\gamma}x^p_{n-2}$ }$ - E.M. Elsayed, H. El-Metwally, Stability and Solutions for Rational Recursive Sequence of Order Three, Journal of Computational Analysis and Applications 17 (2014), 305-315.
-
M.E. Erdogan, C. Cinar and I. Yalcinkaya, On the dynamics of the recursive sequence
$x_{n+1}$ =$\frac{ , Computers & Mathematics with Applications 61 (2011), 533-537. https://doi.org/10.1016/j.camwa.2010.11.030${\alpha}x_{n-1}$ }{${\beta}+{\gamma}x^2_{n-2}x_{n-4}+{\gamma}x_{n-2}x^2_{n-4}$ }$ -
T.F. Ibrahim, On the third order rational difference equation
$x_{n+1}$ =$\frac{ , Int. J. Contemp. Math. Sciences 4 (2009), 1321-1334.$x_nx_{n-2}$ }{$x_{n-1}(a+bx_nx_{n-2}$ }$ - R. Karatas, Global behaviour of a higher order difference equation, Computers & Mathematics with Applications 60 (2010), 830-839. https://doi.org/10.1016/j.camwa.2010.05.030
- M.R.S. Kulenovic, G. Ladas. Dynamics of second order rational difference equations: with open problems and conjectures. CRC Press, 2001.
- M.R.S. Kulenovic, and O. Merino, Discrete dynamical systems and difference equations with Mathematica. CRC Press, 2002.
- M.A. Obaid, E.M. Elsayed and M.M. El-Dessoky, Global Attractivity and Periodic Character of Difference Equation of Order Four, Discrete Dynamics in Nature and Society 2012, Article ID:746738.
- H. Sedaghat, Global behaviours of rational difference equations of orders two and three with quadratic terms, Journal of Difference Equations and Applications 15 (2009), 215-224. https://doi.org/10.1080/10236190802054126
- M. Shojaei, R. Saadati, H. Adibi, Stability and periodic character of a rational third order difference equation, Chaos Solitons and Fractals 39 (2009), 1203-1209. https://doi.org/10.1016/j.chaos.2007.06.029
-
S. Stevic, On the difference equation xn =
$x_n$ =$\frac{ , Applied Mathematics and Computation 218 (2012), 6291-6296. https://doi.org/10.1016/j.amc.2011.11.107$x_{n-k}$ }{$b+cx_{n-1}{\cdot}{\cdot}{\cdot}x-{n-k}$ }$ - N. Taskara, K. Uslu and D.T. Tollu, The periodicity and solutions of the rational difference equation with periodic coefficients, Computers & Mathematics with Application 62 (2011), 1807-1813. https://doi.org/10.1016/j.camwa.2011.06.024
- N. Taskara, D.T. Tollu, Y. Yazlik, Solutions of Rational Difference System of Order Three in terms of Padovan numbers, Journal of Advanced Research in Applied Mathematic 7 (2015), 18-29.
- D.T. Tollu, Y. Yazlik and N. Taskara, On the Solutions of two special types of Riccati Difference Equation via Fibonacci Numbers, Advances in Difference Equations 2013 (2013), 2013:174. https://doi.org/10.1186/1687-1847-2013-174
- D.T. Tollu, Y. Yazlik and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics and Computation 233 (2014), 310-319. https://doi.org/10.1016/j.amc.2014.02.001
- N. Touafek and E.M. Elsayed, On the periodicity of some systems of nonlinear difference equations, Bull. Math. Soc. Sci. Math. Roumanie 55 (2012), 217-224.
- N. Touafek, On a second order rational difference equation, Hacettepe Journal of Mathematics and Statistics 41 (2012), 867- 874.
- N. Touafek, and E.M. Elsayed, On a second order rational systems of difference equations, Hokkaido Mathematical Journal 44 (2015), 29-45. https://doi.org/10.14492/hokmj/1470052352
- I. Yalcinkaya, C. Cinar, and D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis 87 (2008), 689-699. https://doi.org/10.1080/00036810802163279
- I. Yalcinkaya, On the Global Asymptotic Stability of a Second-Order System of Difference Equations, Discrete Dyn. Nat. Soc. 2008 Article ID 860152, 12 pages.
- I. Yalcinkaya, C. Cinar, and M. Atalay, On the solutions of systems of difference equations, Advances in Difference Equations 9 (2008), Article ID 143943.
- L. Yang, J. Yang, Dynamics of a system of two nonlinear difference equations, International Journal of Contemporary Mathematical Sciences 6 (2011), 209-214.
-
X. Yang, W. Su, B. Chen, G.M. Megson, and D.J. Evans, On the recursive sequence
$x_{n+1}$ =$\frac{ , Applied Mathematics and Computation 162 (2005) 1485-1497. https://doi.org/10.1016/j.amc.2004.03.023$ax_{n-1}+bx_{n-2}$ }{$c+dx_{n-1}x_{n-2}$ }$ - Y. Yazlik, D.T. Tollu, N. Taskara, On the Solutions of Difference Equation Systems with Padovan Numbers, Applied Mathematics 4 (2013), 15-20.
- Y. Yazlik, On the solutions and behavior of rational difference equations, Journal of Computational Analysis and Applications 17 (2014), 584-594.
- Y. Yazlik, E.M. Elsayed and N. Taskara, On the Behaviour of the Solutions of Difference Equation Systems, Journal of Computational Analysis and Applications 16 (2014), 932-941.
- Y. Yazlik, D.T. Tollu, and N. Taskara, On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis & Applications 18 (2015), 166-178.
- Y. Yazlik, D.T. Tollu, and N. Taskara, On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences 38 (2015), 4388-4410. https://doi.org/10.1002/mma.3377
- Y. Yazlik, D.T. Tollu, N. Taskara, On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science & Engineering 43 (2016), 22-32.
-
E.M.E. Zayed and M.A. El-Moneam, On the rational recursive sequence
$x_{n+1}$ =$\frac{ , Communications on Applied Nonlinear Analysis 12 (2005), 15-28.${\alpha}+{\beta}x_n+{\gamma}x_{n-1}$ }{$A+Bx_n+Cx_{n-1}$ }$
Cited by
- Analytic Solutions and Stability of Sixth Order Difference Equations vol.2020, pp.None, 2020, https://doi.org/10.1155/2020/1230979
- QUALITATIVE ANALYSIS OF A FOURTH ORDER DIFFERENCE EQUATION vol.10, pp.4, 2017, https://doi.org/10.11948/20190196
- Global behavior of P-dimensional difference equations system vol.29, pp.5, 2017, https://doi.org/10.3934/era.2021029