Nonstandard Hopf bifurcation in switched

TL;DR

This paper investigates a unique type of Hopf bifurcation in switched systems where stability loss is caused by switching laws rather than eigenvalue crossings, revealing a novel bifurcation mechanism.

Contribution

It introduces the concept of nonstandard generalized Hopf bifurcation driven by switching laws, differing from traditional eigenvalue crossing mechanisms in bifurcation theory.

Findings

Identifies a new bifurcation mechanism in switched systems.

Shows stability loss is linked to switching laws, not eigenvalues.

Provides analysis distinguishing this bifurcation from classical Hopf bifurcation.

Abstract

This paper presents an analysis on nonstandard generalized Hopf bifurcation in a class of switched systems where the lost of stability of linearized systems is not due to the crossing of their complex conjugate eigenvalues but relevant to the switching laws between the subslystems. Thus is remarkably different from the mechanism of the Hopf bifurcation and the generalized Hopf bifurcation studied in the literature.