Laminar Chaos

TL;DR

This paper introduces a new type of chaos called laminar chaos in systems with time-varying delay, characterized by alternating periods of steady output and irregular bursts, with dynamics explained by one-dimensional maps.

Contribution

It reveals and analyzes laminar chaos in delay systems, providing a theoretical framework to understand and tune this behavior using simplified maps.

Findings

Laminar phases exhibit nearly constant output levels.

Chaotic variations occur between laminar phases.

Dynamics can be controlled via derived one-dimensional maps.

Abstract

We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity remains almost constant, but its level varies chaotically from phase to phase. In scalar systems the periodic dynamics of the lengths and the chaotic dynamics of the intensity levels can be understood and also tuned via two one-dimensional maps, which can be deduced from the nonlinearity of the delay equation and from the delay variation, respectively.