Universidad Nacional de Colombia, Fizmako Research Group, Bogotá, Colombia.
Universidad Nacional Autónoma de Chota, Cajamarca, Peru.
ScientificWorldJournal. 2023 Apr 5;2023:8971590. doi: 10.1155/2023/8971590. eCollection 2023.
Inspired by some open conjectures in a rational dynamical system by G. Ladas and Palladino, in this paper, we consider the problem of solving a third-order difference equation. We comment the conjecture by Ladas. A third-order rational difference equation is solved analytically. The solution is compared with the solution to the linearized equation. We show that the solution to the linearized equation is not good, in general. The methods employed here may be used to solve other rational difference equations. The period of the solution is calculated. We illustrate the accuracy of the obtained solutions in concrete examples.
受 G. Ladas 和 Palladino 在一个有理动力系统中提出的一些公开猜想的启发，本文考虑了求解三阶差分方程的问题。我们对 Ladas 的猜想进行了评论。三阶有理差分方程被解析地求解。将解与线性化方程的解进行比较。我们表明，线性化方程的解通常不好。这里使用的方法可用于求解其他有理差分方程。计算了解的周期。我们在具体例子中说明了所得到的解的准确性。
