# Analysis of Exact Solutions to Some Systems of Difference Equations

• Mohammed Almatrafi M. B. Almatrafi
• Marwa M. Alzubaidi
Keywords: Difference Equations, Systems of Difference Equations, Exact Solution, Stability, Periodicity

### Abstract

Some nonlinear difference equations can be sometimes solved analytically using manual iteration which begins with some given initial conditions. Obtaining next iterations always depends on the previous ones. Through this paper, we utilize the manual iteration in investigating the exact solutions of the following recursive sequences   $x_{n+1}=\frac{y_{n-5}x_{n-8}}{y_{n-2}(-1-y_{n-5}x_{n-8})},\ \ \ \ \ y_{n+1}% =\frac{x_{n-5}y_{n-8}}{x_{n-2}\left( \pm1\pm x_{n-5}y_{n-8}\right) },$   where the initial conditions $x_{\delta},\ y_{\delta},\ \delta\in \{0,1,...,8\}$ are non-zero real numbers. Some numerical solutions are also presented in some figures to show the behaviour of the solutions.

### References

L.Brailovsky, Structure of quasi-invariant sets,Arch.Math.,59(1992),322-326.

L.Brailovsky, D.Pasechnix , C.E.Praeger, Subsets close to invarianr subset of quasi-invariant subsets for groupactions ,,Proc.Amer. Math.Soc.,123(1995),2283-2295.

C.E.Praeger,On permutation groups with bounded movement,J.Algebra,144(1991),436-442.

C.E.Praeger, The separation theorem for group actions, in ”ordered Groups and Infinite Groups”(W.charlesHolland, Ed.),Kluwer Academic, Dordrecht/ Boston/ Lond, 1995.

A.Hassani,M.Khayaty,E.I.Khukhro and C.E.Praeger, Transitive permutation groups with bounded movementhaving maximum degree.J. Algebra,214(1999),317-337.

J.R.Cho, P.S.Kim, and C.E.Praeger, The maximal number of orbits of a permutation Group with BoundedMovement,J.Algebra,214(1999),625-630.

P.M.Neumann, The structure of finitary Permutation groups,Arch. Math. (Basel)27(1976),3-17.

B.H.Neumann, Groups covered by permutable subsets,J. London Math soc.,29(1954), 236-248.

P.M.Neumann, C.E.Praeger, On the Movement of permutation Group,J.Algebra,214, (1999)631-635.

Published
2019-08-30
How to Cite
Almatrafi, M., & Alzubaidi, M. M. (2019). Analysis of Exact Solutions to Some Systems of Difference Equations. MathLAB Journal, 3, 96-117. Retrieved from https://purkh.com/index.php/mathlab/article/view/478
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Section
Research Articles