If Amplitude of excitation is low and the critical slowing down is severe this leads to an overdamped response in the dynamical system. According to bifurcation theory, warning signs for a critical transition are often found in the form of a slowing down of the system's response to external perturbations.
The slowing down of the response is a result of the system getting closer to a tipping point. As the system gets closer to a tipping point, the basin of attraction around the current state gets smaller. This makes it more difficult for the system to recover from perturbations, and the system becomes more sensitive to small perturbations.
The slowing down of the response is often accompanied by an increase in noise. The slowing down of the response can also be accompanied by a change in the nature of the attractor. As the system gets closer to a tipping point, the basin of attraction around the current state gets smaller. This can lead to a change in the nature of the attractor, from a stable attractor to an unstable attractor.
A slowing down of the response is a warning sign that a system is approaching a tipping point. If the slowing down is severe, it can lead to an overdamped response, which can be a sign that the system is about to undergo a critical transition.
Good chat, where are the external perturbations measured?
surfkid
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As simple as ABC (Applied Bifurcation Concept)! Thanks for the fascinating narrative and accompanying charts, Grant. What's the basis for excitement and then slowing? How is it critical? Some velocity? I see the increasing price action, compressive excitation/zero amplitude trend, and a seeming increased measure of slowness.