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Global behavior of positive solutions of a third order difference equations system | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 249، دوره 14، شماره 1، فروردین 2023، صفحه 3189-3200 اصل مقاله (453.48 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28701.3970 | ||
| نویسنده | ||
| Phong Nam Mai* | ||
| Department of Mathematical Analysis, University of Transport and Communications, Hanoi, Vietnam | ||
| تاریخ دریافت: 23 مهر 1401، تاریخ بازنگری: 14 دی 1401، تاریخ پذیرش: 22 دی 1401 | ||
| چکیده | ||
| In this paper, we investigate the global behavior of positive solutions of the system of difference equations \begin{equation*} x_{n+1}=\alpha+ \dfrac{y^p_{n}}{y^p_{n-2}},\ y_{n+1}=\alpha+ \dfrac{x^q_{n} }{x^q_{n-2}}, \ n=0, 1, 2, ... \end{equation*} where parameters $\alpha, p, q \in (0, \infty)$ and the initial values $x_{i}$, $y_{i}$ are arbitrary positive numbers for $ i= -2,-1, 0$. Moreover, the rate of convergence of positive solutions is established and some numerical examples are given to demonstrate our theoretical results. | ||
| کلیدواژهها | ||
| Difference equation؛ semi-cycle؛ equilibrium؛ boundedness؛ global asymptotic stability؛ rate of convergence | ||
| مراجع | ||
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[1] Q. Din, On the system of rational difference equations, Demonstr. Math. 47 (2014), no. 2, 324–335. [2] Q. Din, T.F. Ibrahim and K.A. Khan, Behavior of a competitive system of second order difference equations, Sci. World J. 2014 (2014) doi: 10.1155/2014/283982. [3] S. Elaydi, An Introduction to Difference Equations, 2 nd edition, Springer-Verlag, NewYork, 1999. [4] S. Elaydi, Discrete Chaos: With Applications in Science and Engineering, Chapman and Hall/CRC, Boka Raton, FL, 2007. [5] M. G¨um¨u¸s, The global asymptotic stability of a system of difference equations, J. Differ. Equ. Appl. 24 (2018), no. 6, 976–991. [6] Y. Halim, M. Berkal and A. Khelifa, On a three-dimensional solvable system of difference equations, Turk. J. Math. 44 (2020), no. 4, 1263–1288. [7] M. Kara and Y. Yazlik, On a solvable system of rational difference equations of higher order, Turk. J. Math. 46(2022), no. 2, 587–611. [8] V.L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Kluwer Academic, Dordrecht, 1993. [9] M. Pituk, More on Poincare’s and Peron’s theorems for difference equations, J. Differ. Equ. Appl. 8 (2002), 201–216. [10] C. Mylona, G. Papaschinopoulos and C.J. Schinas, Stability and flip bifurcation of a three-dimensional exponential system of difference equations, Math. Methods Appl. Sci. 2020 (2020), 1–14. [11] A. Razani, An iterative process of generalized Lipschitizian mappings in the uniformly convex Banach spaces, Miskolc Math. Notes 22 (2021), no. 2, 889–901. [12] S. Stevi´c, MA. Alghamdi, A. Alotaibi and N. Shahzad, On a nonlinear second order system of difference equations, Appl. Math. Comput. 219 (2013), 11388–11394. [13] S. Stevi´c, On the system of difference equations xn = xn−1yn−2 ayn−2+byn−1, yn = yn−1xn−2 cxn−2+dxn−1, Appl. Math. Comput. 270 (2015), 688–704. [14] S. Stevi´c, New class of solvable systems of difference equations, Appl. Math. Lett. 63 (2017), 137–144 . [15] S. Stevi´c, B. Iricanin and Z. Smarda, On a symmetric bilinear system of difference equations, Appl. Math. Lett. 89 (2019), 15–21. [16] S. Stevi´c, B. IriCanin, W. Kosmala and Z. Smada, Note on a solution form to the cyclic bilinear system of difference equations, Appl. Math. Lett. 111 (2021), 106690. [17] E. Ta¸sdemir, On the global asymptotic stability of a system of difference equations with quadratic terms, J. Appl. Math. Comput. 66 (2021), 423–437. [18] E. Ta¸sdemir, M. G¨ocen and Y. Soykan, Global dynamical behaviours and periodicity of a certain quadratic-rational difference equation with delay, Miskolc Math. Notes 23 (2022), 471–484. [19] D.T. Tollua, Y. Yazlikb and N. Taskarac, On fourteen solvable systems of difference equations, Appl. Math. Comput. 233 (2014), 310–319. [20] I. Yalcinkaya, On the Global Asymptotic Stability of a Second-Order System of Difference Equations, Discrete Dyn. Nat. Soc. 2008 (2008), doi: 10.1155/2008/860152. | ||
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