Strange attractors in periodically-kicked degenerate Hopf bifurcations

TL;DR

This paper demonstrates that periodic forcing can transform stable spiral sinks into observable chaotic strange attractors in systems undergoing degenerate Hopf bifurcations, using advanced rank one map theory.

Contribution

It introduces a new multi-parameter approach to rank one maps, showing how periodic kicks induce chaos in degenerate Hopf bifurcations.

Findings

Stable foci can become strange attractors under periodic forcing.

The phenomenon is demonstrated in degenerate supercritical Hopf bifurcations.

The approach extends the theory of rank one maps to multiple parameters.

Abstract

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.