Stability Conditions for a Nonlinear Time Series Model

This research aims to determine whether the proposed time series model is stable or not. To achieve this, Ozaki’s approximation method was utilized, where the nonlinear part is a function that approaches zero, similar to Ozaki’s imposed function. The study produced examples of both stable and unstable models, and it was discovered that the stability and instability of the model are affected by the enforced optional constants. The researchers used the approximation method to obtain an asymptotic linear model that satisfied the singular point of the proposed model. The study first identified the singular points of the suggested model and then focused on determining the stability conditions, which was the main objective of the study. Last, the stability conditions of the limit cycle were established.