Stability problem for non-autonomous systems of non-linear difference equations

AUTHOR(S):

Aleksandr Andreev, Olga Peregudova, Katherine Sutyrkina

TITLE

Stability Problem for Non-autonomous Systems of Non-linear Difference Equations

ABSTRACT

In this paper, a novel approach to the asymptotic stability problem for non-autonomous nonlinear difference equations is presented. We propose a quasi-invariance principle to solve a positive limit set localization problem for such equations. Asymptotic stability proof of the zero solution of non-autonomous difference equation is given by constructing the Lyapunov vector function and comparison system and using the proposed quasi-invariance principle for non-autonomous systems of difference equations. We illustrate the implementation of the proposed approach using the examples of some discrete epidemic models.

KEYWORDS

Non-autonomous systems, non-linear systems, non-linear difference equations

Cite this paper

Aleksandr Andreev, Olga Peregudova, Katherine Sutyrkina. (2019) Stability problem for non-autonomous systems of non-linear difference equations. International Journal of Mathematical and Computational Methods, 4, 58-66