TY  - JOUR
T1  - Dynamics of the rational difference equations
AU  - Oğul, Burak
PY  - 2024
DA  - December
Y2  - 2024
DO  - 10.51354/mjen.1420761
JF  - MANAS Journal of Engineering
JO  - MJEN
PB  - Kyrgyz-Turkish Manas University
WT  - DergiPark
SN  - 1694-7398
SP  - 177
EP  - 184
VL  - 12
IS  - 2
LA  - en
AB  - Discrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work’s validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. nIn this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial valueb 𝑥𝑛+1 = 𝑥𝑛𝑥𝑛−8 ±𝑥𝑛−7 ± 𝑥𝑛𝑥𝑛−7𝑥𝑛−8 , 𝑛 ∈ N0.
KW  - Equilibrium
point
KW  - solution of difference
equation
KW  - stability
KW  - boundedness
KW  - global asymptotic stability
*Corresponding
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UR  - https://doi.org/10.51354/mjen.1420761
L1  - https://dergipark.org.tr/en/download/article-file/3664051
ER  -