The Solution and Dynamic Behaviour of Difference Equations of Twenty-First Order

Abstract

We explore the dynamics of adhering to rational difference formula
 $$ \psi_{m+1}=\frac{\psi_{m-20}}{\pm 1 \pm \psi_{m-2}\psi_{m-5}\psi_{m-8}\psi_{m-11}\psi_{m-14}\psi_{m-17}\psi_{m-20}}, \quad m \in \mathbb{N}_{0} $$
 where the initials are arbitrary nonzero real numbers. Specifically, we examine global asymptotically stability. Additionally, we provide examples and solutions graphs of some special cases.