BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENCE EQUATION

다국어 초록 (Multilingual Abstract)

In this paper we deal with the difference equation yn+1 =ayn−1bynyn−1 + cyn−1yn−2 + d, n ∈ N0, where the coefficients a, b, c, d are positive real numbers and the initial conditions y−2, y−1, y0 are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

참고문헌 (Reference)

1 N. Taskara, "The periodicity and solutions of the rational difference equation with periodic coefficients" 62 : 1807-1813, 2011

2 M. Dehghan, "Stability and periodic character of a third order difference equation" 54 : 2560-2564, 2011

3 M. Shojaei, "Stability and periodic character of a rational third order difference equation" 39 : 1203-1209, 2009

4 E.M. Elsayed, "Stability and Solutions for Rational Recursive Sequence of Order Three" 17 : 305-315, 2014

5 N. Taskara, "Solutions of Rational Difference System of Order Three in terms of Padovan numbers" 7 : 18-29, 2015

6 H. El-Metwally, "Qualitative study of solutions of some difference equations" 2012 : 2012

7 E.M. Elabbasy, "Qualitative properties for a higher order rational difference equation" 33-50, 2013

8 T.F. Ibrahim, "On the third order rational difference equation xn+1 =xnxn 2xn 1(a+bxnxn 2)" 4 : 1321-1334, 2009

9 I. Yalcinkaya, "On the solutions of systems of difference equations" 9 : 2008

10 Y. Yazlik, "On the solutions of a three-dimensional system of difference equations" 43 : 22-32, 2016

11 Y. Yazlik, "On the solutions of a max-type difference equation system" 38 : 4388-4410, 2015

12 Y. Yazlik, "On the solutions and behavior of rational difference equations" 17 : 584-594, 2014

13 X. Yang, "On the recursive sequence xn+1 =axn 1+bxn 2c+dxn 1xn 2" 162 : 1485-1497, 2005

14 A. Andruch-Sobilo, "On the rational recursive sequence xn+1 =axn 1b+cxnxn 1" 43 : 1-9, 2009

15 E.M.E. Zayed, "On the rational recursive sequence xn+1 =+ xn+xn 1A+Bxn+Cxn 1" 12 : 15-28, 2005

16 C. Cinar, "On the positive solutions of the difference equation xn+1 =xn 11+xnxn 1" 150 : 21-24, 2004

17 N. Touafek, "On the periodicity of some systems of nonlinear difference equations" 55 : 217-224, 2012

18 H.M. El-Owaidy, "On the dynamics of the recursive sequence xn+1 =xn 1+xp n 2" 18 : 1013-1018, 2005

19 M.E. Erdogan, "On the dynamics of the recursive sequence xn+1 =xn 1+x2n 2xn 4+xn 2x2n 4" 61 : 533-537, 2011

20 S. Stevi´c, "On the difference equation xn =xn k b+cxn 1 xn k" 218 : 6291-6296, 2012

21 Y. Yazlik, "On the behaviour of solutions for some systems of difference equations" 18 : 166-178, 2015

22 R. Abu-Saris, "On the asymptotic stability of xn+1 =a+xnxn k xn+xn k" 56 : 1172-1175, 2008

23 D.T. Tollu, "On the Solutions of two special types of Riccati Difference Equation via Fibonacci Numbers" 2013 : 174-, 2013

24 Y. Yazlik, "On the Solutions of Difference Equation Systems with Padovan Numbers" 4 : 15-20, 2013

25 I. Yalcinkaya, "On the Global Asymptotic Stability of a Second-Order System of Difference Equations" 2008 :

26 Y. Yazlik, "On the Behaviour of the Solutions of Difference Equation Systems" 16 : 932-941, 2014

27 D.T. Tollu, "On fourteen solvable systems of difference equations" 233 : 310-319, 2014

28 N. Touafek, "On a second order rational systems of difference equations" 44 : 29-45, 2015

29 N. Touafek, "On a second order rational difference equation" 41 : 867-874, 2012

30 H. Sedaghat, "Global behaviours of rational difference equations of orders two and three with quadratic terms" 15 : 215-224, 2009

31 I. Bajo, "Global behaviour of a second-order nonlinear difference equation" 17 : 1471-1486, 2011

32 R. Karatas, "Global behaviour of a higher order difference equation" 60 : 830-839, 2010

33 I. Yalcinkaya, "Global asymptotic stability of a system of difference equations" 87 : 689-699, 2008

34 M.A. Obaid, "Global Attractivity and Periodic Character of Difference Equation of Order Four" 2012 :

35 M.R.S. Kulenovic, "Dynamics of second order rational difference equations: with open problems and conjectures" CRC Press 2001

36 L. Yang, "Dynamics of a system of two nonlinear difference equations" 6 : 209-214, 2011

37 E. Camouzis, "Dynamics of Third-order Rational Difference Equations with Open Problems and Conjectures, Volume 5 of Advances in Discrete Mathematics and Applications" Chapman & Hall/CRC 2008

38 M.R.S. Kulenovic, "Discrete dynamical systems and difference equations with Mathematica" CRC Press 2002