From limit cycles to strange attractors

TL;DR

This paper introduces a quantitative measure of shear in limit cycles and demonstrates how sufficient shear under periodic forcing leads to the emergence of strange attractors and observable chaos.

Contribution

It defines a new quantitative notion of shear for limit cycles and proves the emergence of strange attractors and SRB measures under periodic drives.

Findings

Strain cycles with sufficient shear produce strange attractors.

Periodic pulsatile drives induce sustained chaos.

Strange attractors have well-defined dynamical properties.

Abstract

We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange attractors possess a number of precisely-defined dynamical properties that together imply chaos that is both sustained in time and physically observable.