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SUMMARY:Probability of rate-induced tipping in two slow–fast stochastic 
 mechanical systems
DTSTART:20260108T130000Z
DTEND:20260108T140000Z
DTSTAMP:20260606T020500Z
UID:indico-event-15474@indico.math.cnrs.fr
DESCRIPTION:Speakers: Baptiste Bergeot (INSA CVL)\n\nRate-induced tipping 
 refers to a large and sudden shift\, or critical transition\, in the behav
 ior of a dynamical system when a parameter changes at a speed exceeding a 
 critical rate. Primarily studied in conceptual climate models\, it remains
  largely unexplored in engineering\, despite possible dramatic effects whi
 ch are not predicted (and even unsuspected) with a constant-parameter bifu
 rcation analysis.\nThis presentation explores the impact of noise on rate-
 induced tipping in two types of fast–slow mechanical systems. The first 
 system is a self-sustained reed musical instrument (such as the clarinet) 
 in which one of the bifurcation parameters – specifically\, the pressure
  inside the musician’s mouth – varies slowly over time accounting for 
 attack transients performed by the musician. The second system is a nonlin
 ear passive vibration absorber\, referred to as a Nonlinear Energy Sink (N
 ES)\, which is coupled to a self-sustained oscillator (SSO) requiring vibr
 ation attenuation. \nAlthough these two systems differ greatly in terms o
 f their applications\, they indeed both exhibit rate-induced tipping: when
  a critical tipping point is crossed\, the reed instrument can abruptly tr
 ansition from silence to a musical note\, while the SSO–NES system can s
 witch from mitigated to unmitigated responses. Moreover\, both systems are
  modeled by differential equations containing a small parameter that highl
 ights their singularly perturbed\, fast–slow nature. As a result\, their
  dynamics (i) cannot be fully explained by the concepts traditionally used
  in engineering such as bifurcation diagrams and basins of attraction and 
 (ii) can be significantly influenced by the presence of noise. For each of
  these systems\, the deterministic dynamics will first be described. Subse
 quently\, the influence of noise will be analyzed using both numerical sim
 ulations and analytical methods. The aim is\, for each system\, to estimat
 e the probability of tipping\, a quantity that\, in the deterministic case
 \, abruptly changes from zero to one when the tipping point is crossed.\n\
 nhttps://indico.math.cnrs.fr/event/15474/
LOCATION:Salle de Séminaires (Orléans)
URL:https://indico.math.cnrs.fr/event/15474/
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