论文信息 - Global behavior of third order system of rational difference equations

Global behavior of third order system of rational difference equations

In this paper, our aim is to study the dynamical behavior of third-order system of rational difference equations xn+1 = αxn−2 β + γxnxn−1xn−2 , yn+1 = α1yn−2 β1 + γ1ynyn−1yn−2 , n = 0, 1, · · · . where the parameters α, β, γ, α1, β1, γ1 and initial conditions x0, x−1, x−2, y0, y−1, y−2 are positive real numbers. Some numerical examples are given to verify our theoretical results.

E. Elsayed | Eduardo Liz | I. Yalçinkaya | E. Pilav | M. Kulenovic

[1] Qianhong Zhang,et al. Dynamics of a system of rational third-order difference equation , 2012 .

[2] E. M. Elsayed,et al. On the solutions of systems of rational difference equations , 2012, Math. Comput. Model..

[3] Stevo Stevic,et al. On a third-order system of difference equations , 2012, Appl. Math. Comput..

[4] S. Kalabušić,et al. Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type , 2011 .

[5] Cengiz Çinar,et al. On the behavior of positive solutions of the system of rational difference equations xn+1 = xn-1/(ynxn-1+1), yn+1 = yn-1/(xnyn-1+1) , 2011, Math. Comput. Model..

[6] I. Bajo,et al. Global behaviour of a second-order nonlinear difference equation , 2009, 0905.3642.

[7] Cengiz Çinar,et al. On the positive solutions of the difference equation system xn+1 = 1/yn, yn+1 = yn/xn-1yn-1 , 2004, Appl. Math. Comput..

[8] E. Elsayed,et al. On the periodicity of some systems of nonlinear difference equations , 2012 .

[9] Stevo Stevic,et al. On some solvable systems of difference equations , 2012, Appl. Math. Comput..

[10] S. Kalabušić,et al. Global Dynamics of a Competitive System of Rational Difference Equations in the Plane , 2009 .