  A new type of chaos called laminar chaos was found in singularly perturbed
dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120,
084102 (2018)]. It is characterized by nearly constant laminar phases, which
are periodically interrupted by irregular bursts, where the intensity levels of
the laminar phases vary chaotically from phase to phase. In this paper, we
demonstrate that laminar chaos can also be observed in systems with
quasiperiodic delay, where we generalize the concept of conservative and
dissipative delays to such systems. It turns out that the durations of the
laminar phases vary quasiperiodically and follow the dynamics of a torus map in
contrast to the periodic variation observed for periodic delay. Theoretical and
numerical results indicate that introducing a quasiperiodic delay modulation
into a time-delay system can lead to a giant reduction of the dimension of the
chaotic attractors. By varying the mean delay and keeping other parameters
fixed, we found that the Kaplan-Yorke dimension is modulated quasiperiodically
over several orders of magnitudes, where the dynamics switches
quasiperiodically between different types of high- and low-dimensional types of
chaos.
