Closed-form solutions of a new class of three-dimensional nonlinear difference equations

This paper explored a new three-dimensional nonlinear system of difference equations, capturing intricate dynamic interactions through advanced analytical and computational methods. By employing strategic transformations and analyzing the system's characteristic polynomial roots, we derived exact closed-form solutions for both distinct and repeated root scenarios. Numerical examples were used to validate the theoretical results and demonstrate that even small variations in initial conditions can induce markedly different dynamical behaviors, ranging from stable oscillations to divergent trajectories.