A Short Communication on the Asymptotic Behaviour of the Linear System 𝑥= -x

Abstract: This short communication examines the asymptotic behaviour of the scalar linear differential equation 𝑥̇ = −x. Despite its simplicity, it serves as a canonical model for exponential decay and global asymptotic stability in dynamical systems theory. The analysis includes an explicit solution, phase-line representation, and its role as a local linearization prototype for nonlinear systems. Keywords: asymptotic behavior, canonical model, global asymptotic, dynamical systems theory. Title: A Short Communication on the Asymptotic Behaviour of the Linear System 𝑥̇= -x Author: Ogbonna Nnamuchi International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 14, Issue 1, April 2026 - September 2026 Page No: 25-26 Research Publish Journals Website: www.researchpublish.com Published Date: 30-April-2026 DOI: https://doi.org/10.5281/zenodo.19946845 Paper Download Link (Source) https://www.researchpublish.com/papers/a-short-communication-on-the-asymptotic-behaviour-of-the-linear-system---x