Normal Hyperbolicity in Secondary Hopf Bifurcations

TL;DR

This paper proves that tori formed in secondary Hopf bifurcations are normally hyperbolic and provides conditions for their bifurcation in perturbed systems using averaging methods.

Contribution

It combines existing results to establish normal hyperbolicity of tori in secondary Hopf bifurcations and applies this to systems with small periodic perturbations.

Findings

Tori in secondary Hopf bifurcations are normally hyperbolic.

Sufficient conditions for bifurcation of normally hyperbolic invariant tori are provided.

Application of averaging method to perturbed systems with small time-periodic perturbations.

Abstract

We combine results available in the literature to prove that the torus emerging in a secondary Hopf bifurcation is normally hyperbolic. This result is then applied to establish sufficient conditions for the bifurcation of normally hyperbolic invariant tori in the extended phase space of systems with small time-periodic perturbations via an application of the averaging method.