Domain of attraction of asymptotically stable periodic solutions obtained via averaging principle

TL;DR

This paper presents a method to evaluate the domain of attraction for stable periodic solutions derived using the averaging principle, including extensions to nonsmooth systems.

Contribution

It introduces an approach to assess the domain of attraction for stable periodic solutions obtained via averaging, extending to nonsmooth systems.

Findings

Method effectively evaluates the domain of attraction.

Extension to nonsmooth systems broadens applicability.

Provides theoretical insights into stability regions.

Abstract

In this paper we propose an approach to evaluate the domain of attraction of asymptotically stable periodic solutions obtained via averaging principle (second Bogolubov's theorem or Mel'nikov's method). We discuss also how this result is extended in the case when the right hand part is nonsmooth.