Laminar Chaos in a Mackey-Glass feedback circuit with Variable Time-Delay

Laminar chaos is a newly discovered chaotic behavior theoretically predicted in 2018 [1], which can be characterized by steady-state phases separated by short and irregular burst-like transitions. It has been observed experimentally in an optoelectronic variable time-delay feedback system implemented with a field-programmable gate array (FPGA) [2]. The Mackey-Glass model, developed to simulate the physiological mechanism of red blood cells, is a common time-delay system that can yield a wide range of periodic and chaotic dynamics. We report here the observation of laminar chaos in an electronic Mackey-Glass feedback circuit, the first observation of its kind, implemented with an Arduino board to produce variable time delays. This unique system implementation allows us to easily create audio signals from laminar chaos that contrast with signals generated by a system with a constant time delay.

[1] D. Müller, A. Otto, and G. Radons, Phys. Rev. Lett. 120, 084102 (2018)
[2] J. Hart, R. Roy, D. Müller, A. Otto, and G. Radons,123, Phys. Rev. Lett. 123, 154101 (2019)