@article{Al Ghafli2025, 
author = {Ahmed A. Al Ghafli},
title = {Closed-form solutions of a nonlinear bidimensional difference system via generalized Fibonacci sequences},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {26545-26567},
keywords = {nonlinear difference equations, closed form solutions, d-Fibonacci sequence, system of difference equations},
url = {https://www.sciopen.com/article/10.3934/math.20251167},
doi = {10.3934/math.20251167},
abstract = {This paper presents a new model for a two-dimensional nonlinear difference system that incorporates symmetric interactions between two sequences through a scaling parameter    d and a continuous one-to-one transformation function    f. Explicit analytical solutions are derived, establishing a direct connection with the    d-Fibonacci sequence. The transformation function    f plays a crucial role: It accommodates diverse nonlinear iteration patterns and provides a natural mechanism for regulating both growth dynamics and sequence interactions. Moreover, the use of a continuous one-to-one function guarantees that the analytical solutions of transformed systems can be recovered through its inverse mapping. The approach highlights a unified framework linking generalized Fibonacci-type recursions with nonlinear transformations, offering new insights into the structure and solvability of higher-order discrete systems. Several illustrative examples are provided to support the theoretical findings.}
}