Malaysian Journal of Mathematical Sciences, June 2023, Vol. 17, No. 2
On the Local Stability of a Certain Class of Polynomial Differential System
Mirumbe, I., Nakakawa, J. N., and Mango, J. M.
Corresponding Email: ismail.mirumbe@mak.ac.ug
Received date: 22 February 2022
Accepted date: 22 January 2023
Abstract:
We state and prove a condition for the local stability of a certain class of two dimensional system of polynomial differential equations. We give some examples of polynomial differential systems of equations to demonstrate that this local stability condition established for the trivial equilibrium point $(0, 0)$ is quite sharp and compare our result with the well known Lyapunov local stability criterion (Lyapunov's second method).
Keywords: equilibrium; stability; asymptotic stability; differential system
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