Laminar chaos

Dynamical systems with time-delay arise in many fields such as life science, climate dynamics, synchronization of networks and engineering. In nature the delay is typically not constant but rather time-varying, e.g. due to environmental fluctuations. Recently we found that in such systems there exists a dichotomy, which results in drastic differences in the Lyapunov characterisics of the two classes [1, 2].
Here we show, that introducing a time-varying delay can lead to a hitherto unknown 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. Changing parameters of the delay variation causes a repeated switching between high-dimensional turbulent chaos and low-dimensional laminar chaos.
[1] A. Otto, D. Müller and G. Radons, Phys. Rev. Lett. 118, 044104 (2017).
[2] D. Müller, A. Otto and G. Radons, Phys. Rev. E 95, 062214 (2017).