Testing Critical Slowing Down as a Bifurcation Indicator in a Low-Dissipation Dynamical System

Spike propagation in a nanolaser-based optoelectronic neuron

“…Although I(t) surpasses J tr , it does so for a short time and, since the nanoLD relaxation time is too long when J is close to o under J tr , the nanoLD is unable to respond properly to real-time changes in I(t). This phenomenon is known as critical slowing down and has been observed in theoretical and experimental problems involving a transcritical bifurcation [46][47][48][49]. As the bifurcation is swept over, the system remains in the now unstable zero state, transitioning to the nonzero state when the control parameter is well above the critical point, regardless of its change rate.…”

“…An optimal bias current to momentarily turn the nanoLD on and produce a short yet high optical pulse is found to be J = 214 µA (panel c), with a relatively long response delay (about 150 ps) as the only drawback, consequence of the critical slowing down that is more notorious since the nanoLD is driven way over the threshold. When the current is lowered, there is no critical slowing down [46,47], and the nanoLD turns off faster than it turned on, thus its short duration (roughly 0.5 ns). For a sufficiently high bias current (over 250 µA), the total current J + I(t) is always above J tr and thus the nanoLD is permanently emitting.…”

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

“…In terms of dynamical systems, such transitions may result from a time-varying parameter that crosses a bifurcation point. In this context, lasers have been used as "toy models" because they allow to perform controlled experiments, to test the capability of new time series analysis tools for providing reliable indicators alerting of incoming bifurcations (e.g., Masoller et al, 2015;Marconi et al, 2020, where the abrupt switching of the polarization of the emitted light and the crossing of the laser threshold were used to analyze the suitability of a well-known indicator-critical slowing down-to provide reliable warning of the dynamical transition).…”

Controlling Microresonator Solitons with the Counter-Propagating Pump

“…The exit from the blockade regime is also sensitive to the chosen value of H + /H − and the scan parameters. Generally, nonlinear dynamics under conditions when a parameter is swept across the bifurcation points is an area of research attracting attention in optics and beyond (see, e.g., [24,25] and references therein). The reverse, i.e., ε-positive to ε-negative, scan shows the much narrower range of the soliton-blockade in the plus field, and no solitons in the minus field (see the right column in Figure 6).…”