Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation

TL;DR

This paper demonstrates that periodic modulation of time lag in delay systems with nonlinearity significantly enhances chaotic diffusion, especially under mode locking conditions, linking Arnold tongue structures to diffusion properties.

Contribution

It reveals for the first time how time lag modulation can dramatically increase diffusion in delay systems and connects this to Arnold tongue structures and laminar chaos.

Findings

Diffusion constant can be increased by several orders of magnitude.

Mode locking and laminar chaos conditions optimize diffusion enhancement.

Enhanced diffusion correlates with reduced system dimensionality.

Abstract

We consider a typical class of systems with delayed nonlinearity, which we show to exhibit chaotic diffusion. It is demonstrated that a periodic modulation of the time-lag can lead to an enhancement of the diffusion constant by several orders of magnitude. This effect is the largest if the circle map defined by the modulation shows mode locking and more specifically, fulfills the conditions for laminar chaos. Thus we establish for the first time a connection between Arnold tongue structures in parameter space and diffusive properties of a delay system. Counterintuitively, the enhancement of diffusion is accompanied by a strong reduction of the effective dimensionality of the system.